http://www.physicsbook.gatech.edu/api.php?action=feedcontributions&feedformat=atom&user=Migitalex 2026-04-26T18:10:28Z User contributions MediaWiki 1.42.7 http://www.physicsbook.gatech.edu/index.php?title=Center_of_Mass&diff=7759 2015-12-02T04:50:59Z

<p>Migitalex: /* Middling */</p> <hr /> <div>Claimed by Alex Huynh (ahuynh9)<br /> <br /> ==The Main Idea==<br /> <br /> The center of mass of an object is the point in space where if a force was applied, the object moves according to Newton's laws without rotation. At the center of mass, the distribution of mass is balanced, and the average of the weighted position coordinates of the distributed mass defines its coordinates. Mechanical calculations are often simplified with respect to the center of mass of objects. [5]<br /> <br /> [[File:Ahuynh5.png]]<br /> <br /> When a force is applied not to the center of mass:<br /> <br /> [[File:Ahuynh6.png]]<br /> ----<br /> <br /> ===A Mathematical Model===<br /> <br /> The position of the center of mass of an object can be found by summating the product of each point mass and its relative linear position and dividing by the sum by the total mass.<br /> <br /> [[File:Ahuynh3.png]]<br /> <br /> This equation can then be extended to three dimensions.<br /> <br /> [[File:Ahuynh1.gif]]<br /> <br /> When calculating the center of mass for a continuous distribution of mass, the expression becomes an infinite sum that can be expressed in the form of an integral. [6]<br /> <br /> [[File:Ahuynh4.gif]]<br /> <br /> ----<br /> <br /> ==Examples==<br /> <br /> ===Simple===<br /> A 10 kg point mass and a 5 kg point mass are connected by a 10 m massless rod.<br /> <br /> [[File:1D_COM.png]]<br /> <br /> Find the center of mass. This is example of a 1-dimensional center of mass problem.<br /> <br /> ====Solution====<br /> First, we will need to establish an origin. For simplicity, we will establish the left end, the position of the 10 kg point mass, as the origin. Relative to the origin, the position of the 10 kg mass is 0 m and the position of the 5 kg mass is 10 m. Placing these values into our formula for 1-dimensional center of mass, we get:<br /> <br /> [[File:1D_COM_SOLN.png]]<br /> <br /> Therefore, the center of mass is 10/3 m from the left end of the rod. It is important to state your distances relative to your stated origin.<br /> <br /> ===Moderate===<br /> 3 point masses are placed on the x-y plane as shown:<br /> <br /> [[File:2D_COM.png]]<br /> <br /> Find the center of mass. This is an example of a 2-dimensional center of mass problem.<br /> <br /> ====Solution====<br /> This problem is similar to the last problem except that we will need to find BOTH the x and y components of the center of mass. Like before, we need to establish an origin. For simplicity, we will establish the lower left corner, the position of the 3 kg mass as the origin. Then, we need to solve the two directions separately. We will start with the x direction. Relative to the origin, the 3 kg mass is at 0 m, the 8 kg mass is at 1 m, and the 4 kg mass is at 2 m. Placing these values into our center of mass of point masses formula, we get:<br /> <br /> [[File:2D_COM_SOLN1.png]]<br /> <br /> Therefore, the center of mass lies 16/15 m from the origin in the x direction.<br /> <br /> Next, we will solve for the y direction. Relative to the origin, the 3 kg mass is at 0 m, the 4 kg mass is at 1 m, and the 8 kg mass is at 2 m. Placing these values into our center of mass of point masses formula, we get:<br /> <br /> [[File:2D_COM_SOLN2.png]]<br /> <br /> Therefore, the center of mass lies 4/3 m from the origin in the y direction.<br /> <br /> The center of mass lies at the coordinates (16/15 m, 4/3 m).<br /> <br /> ===Difficult===<br /> Find the x component of the center of mass of a uniform rod of length L and mass M with continuous, uniform mass. This is an example of a continuous mass problem.<br /> <br /> [[File:Continuous_mass_COM_2.png]]<br /> <br /> ====Solution====<br /> <br /> For this problem, we need to use the continuous mass formula. As shown in the diagram, the dm component can be represented by M/L dx because the mass in the rod is uniformly distributed. Therefore, our equation becomes:<br /> <br /> [[File:Continuous_mass_COM_soln1.png]]<br /> <br /> Therefore, the center of mass lies at L/2, which agrees with the rule of symmetry for uniform masses.<br /> <br /> ==Connectedness==<br /> The main purpose of using the center of mass is to simplify irregular objects into point masses. Force diagrams are based on this idea, and this aids in the calculation of motion of complex objects. For biomedical engineering majors, we can use the center of mass of body parts in order to simplify the motion of body parts.<br /> <br /> ==History==<br /> <br /> The concept of center of mass was first introduced by Archimedes while he worked to simplify assumptions about gravity that amounted to a uniform field, thus arriving at the mathematical properties of the center of mass. In an experiment, Archimedes observed that the torque exerted on a lever by weights resting at various points along the lever is the same as what it would be if all of the weights were moved to a single point—their center of mass. He developed mathematical techniques for finding the centers of mass of objects of uniform density of various well-defined shapes. [7]<br /> <br /> == See also ==<br /> <br /> ===Further reading===<br /> <br /> Mass [http://www.physicsbook.gatech.edu/Mass]<br /> <br /> Force [http://www.physicsbook.gatech.edu/Net_Force]<br /> <br /> Moment of Inertia [http://www.physicsbook.gatech.edu/The_Moments_of_Inertia]<br /> <br /> Torque [http://www.physicsbook.gatech.edu/Torque]<br /> <br /> ==References==<br /> <br /> PhysicsLab [http://dev.physicslab.org/document.aspx?doctype=3&amp;filename=rotarymotion_centermass.xml]<br /> <br /> HyperPhysics [http://hyperphysics.phy-astr.gsu.edu/hbase/cm.html]<br /> <br /> Wikipedia [https://en.wikipedia.org/wiki/Center_of_mass]<br /> <br /> <br /> [[Category:Momentum]]</div>

Migitalex http://www.physicsbook.gatech.edu/index.php?title=Center_of_Mass&diff=7758 2015-12-02T04:50:27Z

<p>Migitalex: /* The Main Idea */</p> <hr /> <div>Claimed by Alex Huynh (ahuynh9)<br /> <br /> ==The Main Idea==<br /> <br /> The center of mass of an object is the point in space where if a force was applied, the object moves according to Newton's laws without rotation. At the center of mass, the distribution of mass is balanced, and the average of the weighted position coordinates of the distributed mass defines its coordinates. Mechanical calculations are often simplified with respect to the center of mass of objects. [5]<br /> <br /> [[File:Ahuynh5.png]]<br /> <br /> When a force is applied not to the center of mass:<br /> <br /> [[File:Ahuynh6.png]]<br /> ----<br /> <br /> ===A Mathematical Model===<br /> <br /> The position of the center of mass of an object can be found by summating the product of each point mass and its relative linear position and dividing by the sum by the total mass.<br /> <br /> [[File:Ahuynh3.png]]<br /> <br /> This equation can then be extended to three dimensions.<br /> <br /> [[File:Ahuynh1.gif]]<br /> <br /> When calculating the center of mass for a continuous distribution of mass, the expression becomes an infinite sum that can be expressed in the form of an integral. [6]<br /> <br /> [[File:Ahuynh4.gif]]<br /> <br /> ----<br /> <br /> ==Examples==<br /> <br /> ===Simple===<br /> A 10 kg point mass and a 5 kg point mass are connected by a 10 m massless rod.<br /> <br /> [[File:1D_COM.png]]<br /> <br /> Find the center of mass. This is example of a 1-dimensional center of mass problem.<br /> <br /> ====Solution====<br /> First, we will need to establish an origin. For simplicity, we will establish the left end, the position of the 10 kg point mass, as the origin. Relative to the origin, the position of the 10 kg mass is 0 m and the position of the 5 kg mass is 10 m. Placing these values into our formula for 1-dimensional center of mass, we get:<br /> <br /> [[File:1D_COM_SOLN.png]]<br /> <br /> Therefore, the center of mass is 10/3 m from the left end of the rod. It is important to state your distances relative to your stated origin.<br /> <br /> ===Middling===<br /> 3 point masses are placed on the x-y plane as shown:<br /> <br /> [[File:2D_COM.png]]<br /> <br /> Find the center of mass. This is an example of a 2-dimensional center of mass problem.<br /> <br /> ====Solution====<br /> This problem is similar to the last problem except that we will need to find BOTH the x and y components of the center of mass. Like before, we need to establish an origin. For simplicity, we will establish the lower left corner, the position of the 3 kg mass as the origin. Then, we need to solve the two directions separately. We will start with the x direction. Relative to the origin, the 3 kg mass is at 0 m, the 8 kg mass is at 1 m, and the 4 kg mass is at 2 m. Placing these values into our center of mass of point masses formula, we get:<br /> <br /> [[File:2D_COM_SOLN1.png]]<br /> <br /> Therefore, the center of mass lies 16/15 m from the origin in the x direction.<br /> <br /> Next, we will solve for the y direction. Relative to the origin, the 3 kg mass is at 0 m, the 4 kg mass is at 1 m, and the 8 kg mass is at 2 m. Placing these values into our center of mass of point masses formula, we get:<br /> <br /> [[File:2D_COM_SOLN2.png]]<br /> <br /> Therefore, the center of mass lies 4/3 m from the origin in the y direction.<br /> <br /> The center of mass lies at the coordinates (16/15 m, 4/3 m).<br /> <br /> ===Difficult===<br /> Find the x component of the center of mass of a uniform rod of length L and mass M with continuous, uniform mass. This is an example of a continuous mass problem.<br /> <br /> [[File:Continuous_mass_COM_2.png]]<br /> <br /> ====Solution====<br /> <br /> For this problem, we need to use the continuous mass formula. As shown in the diagram, the dm component can be represented by M/L dx because the mass in the rod is uniformly distributed. Therefore, our equation becomes:<br /> <br /> [[File:Continuous_mass_COM_soln1.png]]<br /> <br /> Therefore, the center of mass lies at L/2, which agrees with the rule of symmetry for uniform masses.<br /> <br /> ==Connectedness==<br /> The main purpose of using the center of mass is to simplify irregular objects into point masses. Force diagrams are based on this idea, and this aids in the calculation of motion of complex objects. For biomedical engineering majors, we can use the center of mass of body parts in order to simplify the motion of body parts.<br /> <br /> ==History==<br /> <br /> The concept of center of mass was first introduced by Archimedes while he worked to simplify assumptions about gravity that amounted to a uniform field, thus arriving at the mathematical properties of the center of mass. In an experiment, Archimedes observed that the torque exerted on a lever by weights resting at various points along the lever is the same as what it would be if all of the weights were moved to a single point—their center of mass. He developed mathematical techniques for finding the centers of mass of objects of uniform density of various well-defined shapes. [7]<br /> <br /> == See also ==<br /> <br /> ===Further reading===<br /> <br /> Mass [http://www.physicsbook.gatech.edu/Mass]<br /> <br /> Force [http://www.physicsbook.gatech.edu/Net_Force]<br /> <br /> Moment of Inertia [http://www.physicsbook.gatech.edu/The_Moments_of_Inertia]<br /> <br /> Torque [http://www.physicsbook.gatech.edu/Torque]<br /> <br /> ==References==<br /> <br /> PhysicsLab [http://dev.physicslab.org/document.aspx?doctype=3&amp;filename=rotarymotion_centermass.xml]<br /> <br /> HyperPhysics [http://hyperphysics.phy-astr.gsu.edu/hbase/cm.html]<br /> <br /> Wikipedia [https://en.wikipedia.org/wiki/Center_of_mass]<br /> <br /> <br /> [[Category:Momentum]]</div>

Migitalex http://www.physicsbook.gatech.edu/index.php?title=Center_of_Mass&diff=7755 2015-12-02T04:49:43Z

<p>Migitalex: /* History */</p> <hr /> <div>Claimed by Alex Huynh (ahuynh9)<br /> <br /> ==The Main Idea==<br /> <br /> The center of mass of an object is the point in space where if a force was applied, the object moves according to Newton's laws without rotation. At the center of mass, the distribution of mass is balanced, and the average of the weighted position coordinates of the distributed mass defines its coordinates. Mechanical calculations are often simplified with respect to the center of mass of objects.<br /> <br /> [[File:Ahuynh5.png]]<br /> <br /> When a force is applied not to the center of mass:<br /> <br /> [[File:Ahuynh6.png]]<br /> ----<br /> <br /> ===A Mathematical Model===<br /> <br /> The position of the center of mass of an object can be found by summating the product of each point mass and its relative linear position and dividing by the sum by the total mass.<br /> <br /> [[File:Ahuynh3.png]]<br /> <br /> This equation can then be extended to three dimensions.<br /> <br /> [[File:Ahuynh1.gif]]<br /> <br /> When calculating the center of mass for a continuous distribution of mass, the expression becomes an infinite sum that can be expressed in the form of an integral.<br /> <br /> [[File:Ahuynh4.gif]]<br /> <br /> ----<br /> <br /> ==Examples==<br /> <br /> ===Simple===<br /> A 10 kg point mass and a 5 kg point mass are connected by a 10 m massless rod.<br /> <br /> [[File:1D_COM.png]]<br /> <br /> Find the center of mass. This is example of a 1-dimensional center of mass problem.<br /> <br /> ====Solution====<br /> First, we will need to establish an origin. For simplicity, we will establish the left end, the position of the 10 kg point mass, as the origin. Relative to the origin, the position of the 10 kg mass is 0 m and the position of the 5 kg mass is 10 m. Placing these values into our formula for 1-dimensional center of mass, we get:<br /> <br /> [[File:1D_COM_SOLN.png]]<br /> <br /> Therefore, the center of mass is 10/3 m from the left end of the rod. It is important to state your distances relative to your stated origin.<br /> <br /> ===Middling===<br /> 3 point masses are placed on the x-y plane as shown:<br /> <br /> [[File:2D_COM.png]]<br /> <br /> Find the center of mass. This is an example of a 2-dimensional center of mass problem.<br /> <br /> ====Solution====<br /> This problem is similar to the last problem except that we will need to find BOTH the x and y components of the center of mass. Like before, we need to establish an origin. For simplicity, we will establish the lower left corner, the position of the 3 kg mass as the origin. Then, we need to solve the two directions separately. We will start with the x direction. Relative to the origin, the 3 kg mass is at 0 m, the 8 kg mass is at 1 m, and the 4 kg mass is at 2 m. Placing these values into our center of mass of point masses formula, we get:<br /> <br /> [[File:2D_COM_SOLN1.png]]<br /> <br /> Therefore, the center of mass lies 16/15 m from the origin in the x direction.<br /> <br /> Next, we will solve for the y direction. Relative to the origin, the 3 kg mass is at 0 m, the 4 kg mass is at 1 m, and the 8 kg mass is at 2 m. Placing these values into our center of mass of point masses formula, we get:<br /> <br /> [[File:2D_COM_SOLN2.png]]<br /> <br /> Therefore, the center of mass lies 4/3 m from the origin in the y direction.<br /> <br /> The center of mass lies at the coordinates (16/15 m, 4/3 m).<br /> <br /> ===Difficult===<br /> Find the x component of the center of mass of a uniform rod of length L and mass M with continuous, uniform mass. This is an example of a continuous mass problem.<br /> <br /> [[File:Continuous_mass_COM_2.png]]<br /> <br /> ====Solution====<br /> <br /> For this problem, we need to use the continuous mass formula. As shown in the diagram, the dm component can be represented by M/L dx because the mass in the rod is uniformly distributed. Therefore, our equation becomes:<br /> <br /> [[File:Continuous_mass_COM_soln1.png]]<br /> <br /> Therefore, the center of mass lies at L/2, which agrees with the rule of symmetry for uniform masses.<br /> <br /> ==Connectedness==<br /> The main purpose of using the center of mass is to simplify irregular objects into point masses. Force diagrams are based on this idea, and this aids in the calculation of motion of complex objects. For biomedical engineering majors, we can use the center of mass of body parts in order to simplify the motion of body parts.<br /> <br /> ==History==<br /> <br /> The concept of center of mass was first introduced by Archimedes while he worked to simplify assumptions about gravity that amounted to a uniform field, thus arriving at the mathematical properties of the center of mass. In an experiment, Archimedes observed that the torque exerted on a lever by weights resting at various points along the lever is the same as what it would be if all of the weights were moved to a single point—their center of mass. He developed mathematical techniques for finding the centers of mass of objects of uniform density of various well-defined shapes. [7]<br /> <br /> == See also ==<br /> <br /> ===Further reading===<br /> <br /> Mass [http://www.physicsbook.gatech.edu/Mass]<br /> <br /> Force [http://www.physicsbook.gatech.edu/Net_Force]<br /> <br /> Moment of Inertia [http://www.physicsbook.gatech.edu/The_Moments_of_Inertia]<br /> <br /> Torque [http://www.physicsbook.gatech.edu/Torque]<br /> <br /> ==References==<br /> <br /> PhysicsLab [http://dev.physicslab.org/document.aspx?doctype=3&amp;filename=rotarymotion_centermass.xml]<br /> <br /> HyperPhysics [http://hyperphysics.phy-astr.gsu.edu/hbase/cm.html]<br /> <br /> Wikipedia [https://en.wikipedia.org/wiki/Center_of_mass]<br /> <br /> <br /> [[Category:Momentum]]</div>

Migitalex http://www.physicsbook.gatech.edu/index.php?title=Center_of_Mass&diff=7752 2015-12-02T04:49:01Z

<p>Migitalex: /* External links */</p> <hr /> <div>Claimed by Alex Huynh (ahuynh9)<br /> <br /> ==The Main Idea==<br /> <br /> The center of mass of an object is the point in space where if a force was applied, the object moves according to Newton's laws without rotation. At the center of mass, the distribution of mass is balanced, and the average of the weighted position coordinates of the distributed mass defines its coordinates. Mechanical calculations are often simplified with respect to the center of mass of objects.<br /> <br /> [[File:Ahuynh5.png]]<br /> <br /> When a force is applied not to the center of mass:<br /> <br /> [[File:Ahuynh6.png]]<br /> ----<br /> <br /> ===A Mathematical Model===<br /> <br /> The position of the center of mass of an object can be found by summating the product of each point mass and its relative linear position and dividing by the sum by the total mass.<br /> <br /> [[File:Ahuynh3.png]]<br /> <br /> This equation can then be extended to three dimensions.<br /> <br /> [[File:Ahuynh1.gif]]<br /> <br /> When calculating the center of mass for a continuous distribution of mass, the expression becomes an infinite sum that can be expressed in the form of an integral.<br /> <br /> [[File:Ahuynh4.gif]]<br /> <br /> ----<br /> <br /> ==Examples==<br /> <br /> ===Simple===<br /> A 10 kg point mass and a 5 kg point mass are connected by a 10 m massless rod.<br /> <br /> [[File:1D_COM.png]]<br /> <br /> Find the center of mass. This is example of a 1-dimensional center of mass problem.<br /> <br /> ====Solution====<br /> First, we will need to establish an origin. For simplicity, we will establish the left end, the position of the 10 kg point mass, as the origin. Relative to the origin, the position of the 10 kg mass is 0 m and the position of the 5 kg mass is 10 m. Placing these values into our formula for 1-dimensional center of mass, we get:<br /> <br /> [[File:1D_COM_SOLN.png]]<br /> <br /> Therefore, the center of mass is 10/3 m from the left end of the rod. It is important to state your distances relative to your stated origin.<br /> <br /> ===Middling===<br /> 3 point masses are placed on the x-y plane as shown:<br /> <br /> [[File:2D_COM.png]]<br /> <br /> Find the center of mass. This is an example of a 2-dimensional center of mass problem.<br /> <br /> ====Solution====<br /> This problem is similar to the last problem except that we will need to find BOTH the x and y components of the center of mass. Like before, we need to establish an origin. For simplicity, we will establish the lower left corner, the position of the 3 kg mass as the origin. Then, we need to solve the two directions separately. We will start with the x direction. Relative to the origin, the 3 kg mass is at 0 m, the 8 kg mass is at 1 m, and the 4 kg mass is at 2 m. Placing these values into our center of mass of point masses formula, we get:<br /> <br /> [[File:2D_COM_SOLN1.png]]<br /> <br /> Therefore, the center of mass lies 16/15 m from the origin in the x direction.<br /> <br /> Next, we will solve for the y direction. Relative to the origin, the 3 kg mass is at 0 m, the 4 kg mass is at 1 m, and the 8 kg mass is at 2 m. Placing these values into our center of mass of point masses formula, we get:<br /> <br /> [[File:2D_COM_SOLN2.png]]<br /> <br /> Therefore, the center of mass lies 4/3 m from the origin in the y direction.<br /> <br /> The center of mass lies at the coordinates (16/15 m, 4/3 m).<br /> <br /> ===Difficult===<br /> Find the x component of the center of mass of a uniform rod of length L and mass M with continuous, uniform mass. This is an example of a continuous mass problem.<br /> <br /> [[File:Continuous_mass_COM_2.png]]<br /> <br /> ====Solution====<br /> <br /> For this problem, we need to use the continuous mass formula. As shown in the diagram, the dm component can be represented by M/L dx because the mass in the rod is uniformly distributed. Therefore, our equation becomes:<br /> <br /> [[File:Continuous_mass_COM_soln1.png]]<br /> <br /> Therefore, the center of mass lies at L/2, which agrees with the rule of symmetry for uniform masses.<br /> <br /> ==Connectedness==<br /> The main purpose of using the center of mass is to simplify irregular objects into point masses. Force diagrams are based on this idea, and this aids in the calculation of motion of complex objects. For biomedical engineering majors, we can use the center of mass of body parts in order to simplify the motion of body parts.<br /> <br /> ==History==<br /> <br /> The concept of center of mass was first introduced by Archimedes while he worked to simplify assumptions about gravity that amounted to a uniform field, thus arriving at the mathematical properties of the center of mass. In an experiment, Archimedes observed that the torque exerted on a lever by weights resting at various points along the lever is the same as what it would be if all of the weights were moved to a single point—their center of mass. He developed mathematical techniques for finding the centers of mass of objects of uniform density of various well-defined shapes.<br /> <br /> == See also ==<br /> <br /> ===Further reading===<br /> <br /> Mass [http://www.physicsbook.gatech.edu/Mass]<br /> <br /> Force [http://www.physicsbook.gatech.edu/Net_Force]<br /> <br /> Moment of Inertia [http://www.physicsbook.gatech.edu/The_Moments_of_Inertia]<br /> <br /> Torque [http://www.physicsbook.gatech.edu/Torque]<br /> <br /> ==References==<br /> <br /> PhysicsLab [http://dev.physicslab.org/document.aspx?doctype=3&amp;filename=rotarymotion_centermass.xml]<br /> <br /> HyperPhysics [http://hyperphysics.phy-astr.gsu.edu/hbase/cm.html]<br /> <br /> Wikipedia [https://en.wikipedia.org/wiki/Center_of_mass]<br /> <br /> <br /> [[Category:Momentum]]</div>

Migitalex http://www.physicsbook.gatech.edu/index.php?title=Center_of_Mass&diff=7750 2015-12-02T04:48:25Z

<p>Migitalex: /* References */</p> <hr /> <div>Claimed by Alex Huynh (ahuynh9)<br /> <br /> ==The Main Idea==<br /> <br /> The center of mass of an object is the point in space where if a force was applied, the object moves according to Newton's laws without rotation. At the center of mass, the distribution of mass is balanced, and the average of the weighted position coordinates of the distributed mass defines its coordinates. Mechanical calculations are often simplified with respect to the center of mass of objects.<br /> <br /> [[File:Ahuynh5.png]]<br /> <br /> When a force is applied not to the center of mass:<br /> <br /> [[File:Ahuynh6.png]]<br /> ----<br /> <br /> ===A Mathematical Model===<br /> <br /> The position of the center of mass of an object can be found by summating the product of each point mass and its relative linear position and dividing by the sum by the total mass.<br /> <br /> [[File:Ahuynh3.png]]<br /> <br /> This equation can then be extended to three dimensions.<br /> <br /> [[File:Ahuynh1.gif]]<br /> <br /> When calculating the center of mass for a continuous distribution of mass, the expression becomes an infinite sum that can be expressed in the form of an integral.<br /> <br /> [[File:Ahuynh4.gif]]<br /> <br /> ----<br /> <br /> ==Examples==<br /> <br /> ===Simple===<br /> A 10 kg point mass and a 5 kg point mass are connected by a 10 m massless rod.<br /> <br /> [[File:1D_COM.png]]<br /> <br /> Find the center of mass. This is example of a 1-dimensional center of mass problem.<br /> <br /> ====Solution====<br /> First, we will need to establish an origin. For simplicity, we will establish the left end, the position of the 10 kg point mass, as the origin. Relative to the origin, the position of the 10 kg mass is 0 m and the position of the 5 kg mass is 10 m. Placing these values into our formula for 1-dimensional center of mass, we get:<br /> <br /> [[File:1D_COM_SOLN.png]]<br /> <br /> Therefore, the center of mass is 10/3 m from the left end of the rod. It is important to state your distances relative to your stated origin.<br /> <br /> ===Middling===<br /> 3 point masses are placed on the x-y plane as shown:<br /> <br /> [[File:2D_COM.png]]<br /> <br /> Find the center of mass. This is an example of a 2-dimensional center of mass problem.<br /> <br /> ====Solution====<br /> This problem is similar to the last problem except that we will need to find BOTH the x and y components of the center of mass. Like before, we need to establish an origin. For simplicity, we will establish the lower left corner, the position of the 3 kg mass as the origin. Then, we need to solve the two directions separately. We will start with the x direction. Relative to the origin, the 3 kg mass is at 0 m, the 8 kg mass is at 1 m, and the 4 kg mass is at 2 m. Placing these values into our center of mass of point masses formula, we get:<br /> <br /> [[File:2D_COM_SOLN1.png]]<br /> <br /> Therefore, the center of mass lies 16/15 m from the origin in the x direction.<br /> <br /> Next, we will solve for the y direction. Relative to the origin, the 3 kg mass is at 0 m, the 4 kg mass is at 1 m, and the 8 kg mass is at 2 m. Placing these values into our center of mass of point masses formula, we get:<br /> <br /> [[File:2D_COM_SOLN2.png]]<br /> <br /> Therefore, the center of mass lies 4/3 m from the origin in the y direction.<br /> <br /> The center of mass lies at the coordinates (16/15 m, 4/3 m).<br /> <br /> ===Difficult===<br /> Find the x component of the center of mass of a uniform rod of length L and mass M with continuous, uniform mass. This is an example of a continuous mass problem.<br /> <br /> [[File:Continuous_mass_COM_2.png]]<br /> <br /> ====Solution====<br /> <br /> For this problem, we need to use the continuous mass formula. As shown in the diagram, the dm component can be represented by M/L dx because the mass in the rod is uniformly distributed. Therefore, our equation becomes:<br /> <br /> [[File:Continuous_mass_COM_soln1.png]]<br /> <br /> Therefore, the center of mass lies at L/2, which agrees with the rule of symmetry for uniform masses.<br /> <br /> ==Connectedness==<br /> The main purpose of using the center of mass is to simplify irregular objects into point masses. Force diagrams are based on this idea, and this aids in the calculation of motion of complex objects. For biomedical engineering majors, we can use the center of mass of body parts in order to simplify the motion of body parts.<br /> <br /> ==History==<br /> <br /> The concept of center of mass was first introduced by Archimedes while he worked to simplify assumptions about gravity that amounted to a uniform field, thus arriving at the mathematical properties of the center of mass. In an experiment, Archimedes observed that the torque exerted on a lever by weights resting at various points along the lever is the same as what it would be if all of the weights were moved to a single point—their center of mass. He developed mathematical techniques for finding the centers of mass of objects of uniform density of various well-defined shapes.<br /> <br /> == See also ==<br /> <br /> ===Further reading===<br /> <br /> Mass [http://www.physicsbook.gatech.edu/Mass]<br /> <br /> Force [http://www.physicsbook.gatech.edu/Net_Force]<br /> <br /> Moment of Inertia [http://www.physicsbook.gatech.edu/The_Moments_of_Inertia]<br /> <br /> Torque [http://www.physicsbook.gatech.edu/Torque]<br /> <br /> ==References==<br /> <br /> ===External links===<br /> <br /> PhysicsLab [http://dev.physicslab.org/document.aspx?doctype=3&amp;filename=rotarymotion_centermass.xml]<br /> <br /> HyperPhysics [http://hyperphysics.phy-astr.gsu.edu/hbase/cm.html]<br /> <br /> Wikipedia [https://en.wikipedia.org/wiki/Center_of_mass]<br /> <br /> <br /> [[Category:Momentum]]</div>

Migitalex http://www.physicsbook.gatech.edu/index.php?title=Center_of_Mass&diff=7746 2015-12-02T04:47:45Z

<p>Migitalex: /* See also */</p> <hr /> <div>Claimed by Alex Huynh (ahuynh9)<br /> <br /> ==The Main Idea==<br /> <br /> The center of mass of an object is the point in space where if a force was applied, the object moves according to Newton's laws without rotation. At the center of mass, the distribution of mass is balanced, and the average of the weighted position coordinates of the distributed mass defines its coordinates. Mechanical calculations are often simplified with respect to the center of mass of objects.<br /> <br /> [[File:Ahuynh5.png]]<br /> <br /> When a force is applied not to the center of mass:<br /> <br /> [[File:Ahuynh6.png]]<br /> ----<br /> <br /> ===A Mathematical Model===<br /> <br /> The position of the center of mass of an object can be found by summating the product of each point mass and its relative linear position and dividing by the sum by the total mass.<br /> <br /> [[File:Ahuynh3.png]]<br /> <br /> This equation can then be extended to three dimensions.<br /> <br /> [[File:Ahuynh1.gif]]<br /> <br /> When calculating the center of mass for a continuous distribution of mass, the expression becomes an infinite sum that can be expressed in the form of an integral.<br /> <br /> [[File:Ahuynh4.gif]]<br /> <br /> ----<br /> <br /> ==Examples==<br /> <br /> ===Simple===<br /> A 10 kg point mass and a 5 kg point mass are connected by a 10 m massless rod.<br /> <br /> [[File:1D_COM.png]]<br /> <br /> Find the center of mass. This is example of a 1-dimensional center of mass problem.<br /> <br /> ====Solution====<br /> First, we will need to establish an origin. For simplicity, we will establish the left end, the position of the 10 kg point mass, as the origin. Relative to the origin, the position of the 10 kg mass is 0 m and the position of the 5 kg mass is 10 m. Placing these values into our formula for 1-dimensional center of mass, we get:<br /> <br /> [[File:1D_COM_SOLN.png]]<br /> <br /> Therefore, the center of mass is 10/3 m from the left end of the rod. It is important to state your distances relative to your stated origin.<br /> <br /> ===Middling===<br /> 3 point masses are placed on the x-y plane as shown:<br /> <br /> [[File:2D_COM.png]]<br /> <br /> Find the center of mass. This is an example of a 2-dimensional center of mass problem.<br /> <br /> ====Solution====<br /> This problem is similar to the last problem except that we will need to find BOTH the x and y components of the center of mass. Like before, we need to establish an origin. For simplicity, we will establish the lower left corner, the position of the 3 kg mass as the origin. Then, we need to solve the two directions separately. We will start with the x direction. Relative to the origin, the 3 kg mass is at 0 m, the 8 kg mass is at 1 m, and the 4 kg mass is at 2 m. Placing these values into our center of mass of point masses formula, we get:<br /> <br /> [[File:2D_COM_SOLN1.png]]<br /> <br /> Therefore, the center of mass lies 16/15 m from the origin in the x direction.<br /> <br /> Next, we will solve for the y direction. Relative to the origin, the 3 kg mass is at 0 m, the 4 kg mass is at 1 m, and the 8 kg mass is at 2 m. Placing these values into our center of mass of point masses formula, we get:<br /> <br /> [[File:2D_COM_SOLN2.png]]<br /> <br /> Therefore, the center of mass lies 4/3 m from the origin in the y direction.<br /> <br /> The center of mass lies at the coordinates (16/15 m, 4/3 m).<br /> <br /> ===Difficult===<br /> Find the x component of the center of mass of a uniform rod of length L and mass M with continuous, uniform mass. This is an example of a continuous mass problem.<br /> <br /> [[File:Continuous_mass_COM_2.png]]<br /> <br /> ====Solution====<br /> <br /> For this problem, we need to use the continuous mass formula. As shown in the diagram, the dm component can be represented by M/L dx because the mass in the rod is uniformly distributed. Therefore, our equation becomes:<br /> <br /> [[File:Continuous_mass_COM_soln1.png]]<br /> <br /> Therefore, the center of mass lies at L/2, which agrees with the rule of symmetry for uniform masses.<br /> <br /> ==Connectedness==<br /> The main purpose of using the center of mass is to simplify irregular objects into point masses. Force diagrams are based on this idea, and this aids in the calculation of motion of complex objects. For biomedical engineering majors, we can use the center of mass of body parts in order to simplify the motion of body parts.<br /> <br /> ==History==<br /> <br /> The concept of center of mass was first introduced by Archimedes while he worked to simplify assumptions about gravity that amounted to a uniform field, thus arriving at the mathematical properties of the center of mass. In an experiment, Archimedes observed that the torque exerted on a lever by weights resting at various points along the lever is the same as what it would be if all of the weights were moved to a single point—their center of mass. He developed mathematical techniques for finding the centers of mass of objects of uniform density of various well-defined shapes.<br /> <br /> == See also ==<br /> <br /> ===Further reading===<br /> <br /> Mass [http://www.physicsbook.gatech.edu/Mass]<br /> <br /> Force [http://www.physicsbook.gatech.edu/Net_Force]<br /> <br /> Moment of Inertia [http://www.physicsbook.gatech.edu/The_Moments_of_Inertia]<br /> <br /> Torque [http://www.physicsbook.gatech.edu/Torque]<br /> <br /> ==References==<br /> <br /> This section contains the the references you used while writing this page<br /> <br /> [[Category:Which Category did you place this in?]]</div>

Migitalex http://www.physicsbook.gatech.edu/index.php?title=Center_of_Mass&diff=7742 2015-12-02T04:46:13Z

<p>Migitalex: /* Connectedness */</p> <hr /> <div>Claimed by Alex Huynh (ahuynh9)<br /> <br /> ==The Main Idea==<br /> <br /> The center of mass of an object is the point in space where if a force was applied, the object moves according to Newton's laws without rotation. At the center of mass, the distribution of mass is balanced, and the average of the weighted position coordinates of the distributed mass defines its coordinates. Mechanical calculations are often simplified with respect to the center of mass of objects.<br /> <br /> [[File:Ahuynh5.png]]<br /> <br /> When a force is applied not to the center of mass:<br /> <br /> [[File:Ahuynh6.png]]<br /> ----<br /> <br /> ===A Mathematical Model===<br /> <br /> The position of the center of mass of an object can be found by summating the product of each point mass and its relative linear position and dividing by the sum by the total mass.<br /> <br /> [[File:Ahuynh3.png]]<br /> <br /> This equation can then be extended to three dimensions.<br /> <br /> [[File:Ahuynh1.gif]]<br /> <br /> When calculating the center of mass for a continuous distribution of mass, the expression becomes an infinite sum that can be expressed in the form of an integral.<br /> <br /> [[File:Ahuynh4.gif]]<br /> <br /> ----<br /> <br /> ==Examples==<br /> <br /> ===Simple===<br /> A 10 kg point mass and a 5 kg point mass are connected by a 10 m massless rod.<br /> <br /> [[File:1D_COM.png]]<br /> <br /> Find the center of mass. This is example of a 1-dimensional center of mass problem.<br /> <br /> ====Solution====<br /> First, we will need to establish an origin. For simplicity, we will establish the left end, the position of the 10 kg point mass, as the origin. Relative to the origin, the position of the 10 kg mass is 0 m and the position of the 5 kg mass is 10 m. Placing these values into our formula for 1-dimensional center of mass, we get:<br /> <br /> [[File:1D_COM_SOLN.png]]<br /> <br /> Therefore, the center of mass is 10/3 m from the left end of the rod. It is important to state your distances relative to your stated origin.<br /> <br /> ===Middling===<br /> 3 point masses are placed on the x-y plane as shown:<br /> <br /> [[File:2D_COM.png]]<br /> <br /> Find the center of mass. This is an example of a 2-dimensional center of mass problem.<br /> <br /> ====Solution====<br /> This problem is similar to the last problem except that we will need to find BOTH the x and y components of the center of mass. Like before, we need to establish an origin. For simplicity, we will establish the lower left corner, the position of the 3 kg mass as the origin. Then, we need to solve the two directions separately. We will start with the x direction. Relative to the origin, the 3 kg mass is at 0 m, the 8 kg mass is at 1 m, and the 4 kg mass is at 2 m. Placing these values into our center of mass of point masses formula, we get:<br /> <br /> [[File:2D_COM_SOLN1.png]]<br /> <br /> Therefore, the center of mass lies 16/15 m from the origin in the x direction.<br /> <br /> Next, we will solve for the y direction. Relative to the origin, the 3 kg mass is at 0 m, the 4 kg mass is at 1 m, and the 8 kg mass is at 2 m. Placing these values into our center of mass of point masses formula, we get:<br /> <br /> [[File:2D_COM_SOLN2.png]]<br /> <br /> Therefore, the center of mass lies 4/3 m from the origin in the y direction.<br /> <br /> The center of mass lies at the coordinates (16/15 m, 4/3 m).<br /> <br /> ===Difficult===<br /> Find the x component of the center of mass of a uniform rod of length L and mass M with continuous, uniform mass. This is an example of a continuous mass problem.<br /> <br /> [[File:Continuous_mass_COM_2.png]]<br /> <br /> ====Solution====<br /> <br /> For this problem, we need to use the continuous mass formula. As shown in the diagram, the dm component can be represented by M/L dx because the mass in the rod is uniformly distributed. Therefore, our equation becomes:<br /> <br /> [[File:Continuous_mass_COM_soln1.png]]<br /> <br /> Therefore, the center of mass lies at L/2, which agrees with the rule of symmetry for uniform masses.<br /> <br /> ==Connectedness==<br /> The main purpose of using the center of mass is to simplify irregular objects into point masses. Force diagrams are based on this idea, and this aids in the calculation of motion of complex objects. For biomedical engineering majors, we can use the center of mass of body parts in order to simplify the motion of body parts.<br /> <br /> ==History==<br /> <br /> The concept of center of mass was first introduced by Archimedes while he worked to simplify assumptions about gravity that amounted to a uniform field, thus arriving at the mathematical properties of the center of mass. In an experiment, Archimedes observed that the torque exerted on a lever by weights resting at various points along the lever is the same as what it would be if all of the weights were moved to a single point—their center of mass. He developed mathematical techniques for finding the centers of mass of objects of uniform density of various well-defined shapes.<br /> <br /> == See also ==<br /> <br /> ===Further reading===<br /> <br /> Mass [http://www.physicsbook.gatech.edu/Mass]<br /> <br /> Force [http://www.physicsbook.gatech.edu/Net_Force]<br /> <br /> Moment of Inertia [http://www.physicsbook.gatech.edu/The_Moments_of_Inertia]<br /> <br /> Torque [http://www.physicsbook.gatech.edu/Torque]<br /> <br /> ===External links===<br /> <br /> PhysicsLab [http://dev.physicslab.org/document.aspx?doctype=3&amp;filename=rotarymotion_centermass.xml]<br /> <br /> HyperPhysics [http://hyperphysics.phy-astr.gsu.edu/hbase/cm.html]<br /> <br /> Wikipedia [https://en.wikipedia.org/wiki/Center_of_mass]<br /> <br /> ==References==<br /> <br /> This section contains the the references you used while writing this page<br /> <br /> [[Category:Which Category did you place this in?]]</div>

Migitalex http://www.physicsbook.gatech.edu/index.php?title=Center_of_Mass&diff=7672 2015-12-02T04:14:44Z

<p>Migitalex: /* Difficult */</p> <hr /> <div>Claimed by Alex Huynh (ahuynh9)<br /> <br /> ==The Main Idea==<br /> <br /> The center of mass of an object is the point in space where if a force was applied, the object moves according to Newton's laws without rotation. At the center of mass, the distribution of mass is balanced, and the average of the weighted position coordinates of the distributed mass defines its coordinates. Mechanical calculations are often simplified with respect to the center of mass of objects.<br /> <br /> [[File:Ahuynh5.png]]<br /> <br /> When a force is applied not to the center of mass:<br /> <br /> [[File:Ahuynh6.png]]<br /> ----<br /> <br /> ===A Mathematical Model===<br /> <br /> The position of the center of mass of an object can be found by summating the product of each point mass and its relative linear position and dividing by the sum by the total mass.<br /> <br /> [[File:Ahuynh3.png]]<br /> <br /> This equation can then be extended to three dimensions.<br /> <br /> [[File:Ahuynh1.gif]]<br /> <br /> When calculating the center of mass for a continuous distribution of mass, the expression becomes an infinite sum that can be expressed in the form of an integral.<br /> <br /> [[File:Ahuynh4.gif]]<br /> <br /> ----<br /> <br /> ==Examples==<br /> <br /> ===Simple===<br /> A 10 kg point mass and a 5 kg point mass are connected by a 10 m massless rod.<br /> <br /> [[File:1D_COM.png]]<br /> <br /> Find the center of mass. This is example of a 1-dimensional center of mass problem.<br /> <br /> ====Solution====<br /> First, we will need to establish an origin. For simplicity, we will establish the left end, the position of the 10 kg point mass, as the origin. Relative to the origin, the position of the 10 kg mass is 0 m and the position of the 5 kg mass is 10 m. Placing these values into our formula for 1-dimensional center of mass, we get:<br /> <br /> [[File:1D_COM_SOLN.png]]<br /> <br /> Therefore, the center of mass is 10/3 m from the left end of the rod. It is important to state your distances relative to your stated origin.<br /> <br /> ===Middling===<br /> 3 point masses are placed on the x-y plane as shown:<br /> <br /> [[File:2D_COM.png]]<br /> <br /> Find the center of mass. This is an example of a 2-dimensional center of mass problem.<br /> <br /> ====Solution====<br /> This problem is similar to the last problem except that we will need to find BOTH the x and y components of the center of mass. Like before, we need to establish an origin. For simplicity, we will establish the lower left corner, the position of the 3 kg mass as the origin. Then, we need to solve the two directions separately. We will start with the x direction. Relative to the origin, the 3 kg mass is at 0 m, the 8 kg mass is at 1 m, and the 4 kg mass is at 2 m. Placing these values into our center of mass of point masses formula, we get:<br /> <br /> [[File:2D_COM_SOLN1.png]]<br /> <br /> Therefore, the center of mass lies 16/15 m from the origin in the x direction.<br /> <br /> Next, we will solve for the y direction. Relative to the origin, the 3 kg mass is at 0 m, the 4 kg mass is at 1 m, and the 8 kg mass is at 2 m. Placing these values into our center of mass of point masses formula, we get:<br /> <br /> [[File:2D_COM_SOLN2.png]]<br /> <br /> Therefore, the center of mass lies 4/3 m from the origin in the y direction.<br /> <br /> The center of mass lies at the coordinates (16/15 m, 4/3 m).<br /> <br /> ===Difficult===<br /> Find the x component of the center of mass of a uniform rod of length L and mass M with continuous, uniform mass. This is an example of a continuous mass problem.<br /> <br /> [[File:Continuous_mass_COM_2.png]]<br /> <br /> ====Solution====<br /> <br /> For this problem, we need to use the continuous mass formula. As shown in the diagram, the dm component can be represented by M/L dx because the mass in the rod is uniformly distributed. Therefore, our equation becomes:<br /> <br /> [[File:Continuous_mass_COM_soln1.png]]<br /> <br /> Therefore, the center of mass lies at L/2, which agrees with the rule of symmetry for uniform masses.<br /> <br /> ==Connectedness==<br /> #How is this topic connected to something that you are interested in?<br /> #How is it connected to your major?<br /> #Is there an interesting industrial application?<br /> <br /> ==History==<br /> <br /> The concept of center of mass was first introduced by Archimedes while he worked to simplify assumptions about gravity that amounted to a uniform field, thus arriving at the mathematical properties of the center of mass. In an experiment, Archimedes observed that the torque exerted on a lever by weights resting at various points along the lever is the same as what it would be if all of the weights were moved to a single point—their center of mass. He developed mathematical techniques for finding the centers of mass of objects of uniform density of various well-defined shapes.<br /> <br /> == See also ==<br /> <br /> ===Further reading===<br /> <br /> Mass [http://www.physicsbook.gatech.edu/Mass]<br /> <br /> Force [http://www.physicsbook.gatech.edu/Net_Force]<br /> <br /> Moment of Inertia [http://www.physicsbook.gatech.edu/The_Moments_of_Inertia]<br /> <br /> Torque [http://www.physicsbook.gatech.edu/Torque]<br /> <br /> ===External links===<br /> <br /> PhysicsLab [http://dev.physicslab.org/document.aspx?doctype=3&amp;filename=rotarymotion_centermass.xml]<br /> <br /> HyperPhysics [http://hyperphysics.phy-astr.gsu.edu/hbase/cm.html]<br /> <br /> Wikipedia [https://en.wikipedia.org/wiki/Center_of_mass]<br /> <br /> ==References==<br /> <br /> This section contains the the references you used while writing this page<br /> <br /> [[Category:Which Category did you place this in?]]</div>

Migitalex http://www.physicsbook.gatech.edu/index.php?title=Center_of_Mass&diff=7665 2015-12-02T04:13:18Z

<p>Migitalex: /* See also */</p> <hr /> <div>Claimed by Alex Huynh (ahuynh9)<br /> <br /> ==The Main Idea==<br /> <br /> The center of mass of an object is the point in space where if a force was applied, the object moves according to Newton's laws without rotation. At the center of mass, the distribution of mass is balanced, and the average of the weighted position coordinates of the distributed mass defines its coordinates. Mechanical calculations are often simplified with respect to the center of mass of objects.<br /> <br /> [[File:Ahuynh5.png]]<br /> <br /> When a force is applied not to the center of mass:<br /> <br /> [[File:Ahuynh6.png]]<br /> ----<br /> <br /> ===A Mathematical Model===<br /> <br /> The position of the center of mass of an object can be found by summating the product of each point mass and its relative linear position and dividing by the sum by the total mass.<br /> <br /> [[File:Ahuynh3.png]]<br /> <br /> This equation can then be extended to three dimensions.<br /> <br /> [[File:Ahuynh1.gif]]<br /> <br /> When calculating the center of mass for a continuous distribution of mass, the expression becomes an infinite sum that can be expressed in the form of an integral.<br /> <br /> [[File:Ahuynh4.gif]]<br /> <br /> ----<br /> <br /> ==Examples==<br /> <br /> ===Simple===<br /> A 10 kg point mass and a 5 kg point mass are connected by a 10 m massless rod.<br /> <br /> [[File:1D_COM.png]]<br /> <br /> Find the center of mass. This is example of a 1-dimensional center of mass problem.<br /> <br /> ====Solution====<br /> First, we will need to establish an origin. For simplicity, we will establish the left end, the position of the 10 kg point mass, as the origin. Relative to the origin, the position of the 10 kg mass is 0 m and the position of the 5 kg mass is 10 m. Placing these values into our formula for 1-dimensional center of mass, we get:<br /> <br /> [[File:1D_COM_SOLN.png]]<br /> <br /> Therefore, the center of mass is 10/3 m from the left end of the rod. It is important to state your distances relative to your stated origin.<br /> <br /> ===Middling===<br /> 3 point masses are placed on the x-y plane as shown:<br /> <br /> [[File:2D_COM.png]]<br /> <br /> Find the center of mass. This is an example of a 2-dimensional center of mass problem.<br /> <br /> ====Solution====<br /> This problem is similar to the last problem except that we will need to find BOTH the x and y components of the center of mass. Like before, we need to establish an origin. For simplicity, we will establish the lower left corner, the position of the 3 kg mass as the origin. Then, we need to solve the two directions separately. We will start with the x direction. Relative to the origin, the 3 kg mass is at 0 m, the 8 kg mass is at 1 m, and the 4 kg mass is at 2 m. Placing these values into our center of mass of point masses formula, we get:<br /> <br /> [[File:2D_COM_SOLN1.png]]<br /> <br /> Therefore, the center of mass lies 16/15 m from the origin in the x direction.<br /> <br /> Next, we will solve for the y direction. Relative to the origin, the 3 kg mass is at 0 m, the 4 kg mass is at 1 m, and the 8 kg mass is at 2 m. Placing these values into our center of mass of point masses formula, we get:<br /> <br /> [[File:2D_COM_SOLN2.png]]<br /> <br /> Therefore, the center of mass lies 4/3 m from the origin in the y direction.<br /> <br /> The center of mass lies at the coordinates (16/15 m, 4/3 m).<br /> <br /> ===Difficult===<br /> Find the x component of the center of mass of a uniform rod of length L and mass M with continuous, uniform mass. This is an example of a continuous mass problem.<br /> <br /> [[File:Continuous_mass_COM_2.png]]<br /> <br /> For this problem, we need to use the continuous mass formula. As shown in the diagram, the dm component can be represented by M/L dx because the mass in the rod is uniformly distributed. Therefore, our equation becomes:<br /> <br /> [[File:Continuous_mass_COM_soln1.png]]<br /> <br /> Therefore, the center of mass lies at L/2, which agrees with the rule of symmetry for uniform masses.<br /> <br /> ==Connectedness==<br /> #How is this topic connected to something that you are interested in?<br /> #How is it connected to your major?<br /> #Is there an interesting industrial application?<br /> <br /> ==History==<br /> <br /> The concept of center of mass was first introduced by Archimedes while he worked to simplify assumptions about gravity that amounted to a uniform field, thus arriving at the mathematical properties of the center of mass. In an experiment, Archimedes observed that the torque exerted on a lever by weights resting at various points along the lever is the same as what it would be if all of the weights were moved to a single point—their center of mass. He developed mathematical techniques for finding the centers of mass of objects of uniform density of various well-defined shapes.<br /> <br /> == See also ==<br /> <br /> ===Further reading===<br /> <br /> Mass [http://www.physicsbook.gatech.edu/Mass]<br /> <br /> Force [http://www.physicsbook.gatech.edu/Net_Force]<br /> <br /> Moment of Inertia [http://www.physicsbook.gatech.edu/The_Moments_of_Inertia]<br /> <br /> Torque [http://www.physicsbook.gatech.edu/Torque]<br /> <br /> ===External links===<br /> <br /> PhysicsLab [http://dev.physicslab.org/document.aspx?doctype=3&amp;filename=rotarymotion_centermass.xml]<br /> <br /> HyperPhysics [http://hyperphysics.phy-astr.gsu.edu/hbase/cm.html]<br /> <br /> Wikipedia [https://en.wikipedia.org/wiki/Center_of_mass]<br /> <br /> ==References==<br /> <br /> This section contains the the references you used while writing this page<br /> <br /> [[Category:Which Category did you place this in?]]</div>

Migitalex http://www.physicsbook.gatech.edu/index.php?title=Center_of_Mass&diff=7658 2015-12-02T04:08:43Z

<p>Migitalex: /* Difficult */</p> <hr /> <div>Claimed by Alex Huynh (ahuynh9)<br /> <br /> ==The Main Idea==<br /> <br /> The center of mass of an object is the point in space where if a force was applied, the object moves according to Newton's laws without rotation. At the center of mass, the distribution of mass is balanced, and the average of the weighted position coordinates of the distributed mass defines its coordinates. Mechanical calculations are often simplified with respect to the center of mass of objects.<br /> <br /> [[File:Ahuynh5.png]]<br /> <br /> When a force is applied not to the center of mass:<br /> <br /> [[File:Ahuynh6.png]]<br /> ----<br /> <br /> ===A Mathematical Model===<br /> <br /> The position of the center of mass of an object can be found by summating the product of each point mass and its relative linear position and dividing by the sum by the total mass.<br /> <br /> [[File:Ahuynh3.png]]<br /> <br /> This equation can then be extended to three dimensions.<br /> <br /> [[File:Ahuynh1.gif]]<br /> <br /> When calculating the center of mass for a continuous distribution of mass, the expression becomes an infinite sum that can be expressed in the form of an integral.<br /> <br /> [[File:Ahuynh4.gif]]<br /> <br /> ----<br /> <br /> ==Examples==<br /> <br /> ===Simple===<br /> A 10 kg point mass and a 5 kg point mass are connected by a 10 m massless rod.<br /> <br /> [[File:1D_COM.png]]<br /> <br /> Find the center of mass. This is example of a 1-dimensional center of mass problem.<br /> <br /> ====Solution====<br /> First, we will need to establish an origin. For simplicity, we will establish the left end, the position of the 10 kg point mass, as the origin. Relative to the origin, the position of the 10 kg mass is 0 m and the position of the 5 kg mass is 10 m. Placing these values into our formula for 1-dimensional center of mass, we get:<br /> <br /> [[File:1D_COM_SOLN.png]]<br /> <br /> Therefore, the center of mass is 10/3 m from the left end of the rod. It is important to state your distances relative to your stated origin.<br /> <br /> ===Middling===<br /> 3 point masses are placed on the x-y plane as shown:<br /> <br /> [[File:2D_COM.png]]<br /> <br /> Find the center of mass. This is an example of a 2-dimensional center of mass problem.<br /> <br /> ====Solution====<br /> This problem is similar to the last problem except that we will need to find BOTH the x and y components of the center of mass. Like before, we need to establish an origin. For simplicity, we will establish the lower left corner, the position of the 3 kg mass as the origin. Then, we need to solve the two directions separately. We will start with the x direction. Relative to the origin, the 3 kg mass is at 0 m, the 8 kg mass is at 1 m, and the 4 kg mass is at 2 m. Placing these values into our center of mass of point masses formula, we get:<br /> <br /> [[File:2D_COM_SOLN1.png]]<br /> <br /> Therefore, the center of mass lies 16/15 m from the origin in the x direction.<br /> <br /> Next, we will solve for the y direction. Relative to the origin, the 3 kg mass is at 0 m, the 4 kg mass is at 1 m, and the 8 kg mass is at 2 m. Placing these values into our center of mass of point masses formula, we get:<br /> <br /> [[File:2D_COM_SOLN2.png]]<br /> <br /> Therefore, the center of mass lies 4/3 m from the origin in the y direction.<br /> <br /> The center of mass lies at the coordinates (16/15 m, 4/3 m).<br /> <br /> ===Difficult===<br /> Find the x component of the center of mass of a uniform rod of length L and mass M with continuous, uniform mass. This is an example of a continuous mass problem.<br /> <br /> [[File:Continuous_mass_COM_2.png]]<br /> <br /> For this problem, we need to use the continuous mass formula. As shown in the diagram, the dm component can be represented by M/L dx because the mass in the rod is uniformly distributed. Therefore, our equation becomes:<br /> <br /> [[File:Continuous_mass_COM_soln1.png]]<br /> <br /> Therefore, the center of mass lies at L/2, which agrees with the rule of symmetry for uniform masses.<br /> <br /> ==Connectedness==<br /> #How is this topic connected to something that you are interested in?<br /> #How is it connected to your major?<br /> #Is there an interesting industrial application?<br /> <br /> ==History==<br /> <br /> The concept of center of mass was first introduced by Archimedes while he worked to simplify assumptions about gravity that amounted to a uniform field, thus arriving at the mathematical properties of the center of mass. In an experiment, Archimedes observed that the torque exerted on a lever by weights resting at various points along the lever is the same as what it would be if all of the weights were moved to a single point—their center of mass. He developed mathematical techniques for finding the centers of mass of objects of uniform density of various well-defined shapes.<br /> <br /> == See also ==<br /> <br /> Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?<br /> <br /> ===Further reading===<br /> <br /> PhysicsLab [http://dev.physicslab.org/document.aspx?doctype=3&amp;filename=rotarymotion_centermass.xml]<br /> <br /> HyperPhysics [http://hyperphysics.phy-astr.gsu.edu/hbase/cm.html]<br /> <br /> Wikipedia [https://en.wikipedia.org/wiki/Center_of_mass]<br /> <br /> ===External links===<br /> <br /> PhysicsLab [http://dev.physicslab.org/document.aspx?doctype=3&amp;filename=rotarymotion_centermass.xml]<br /> <br /> HyperPhysics [http://hyperphysics.phy-astr.gsu.edu/hbase/cm.html]<br /> <br /> Wikipedia [https://en.wikipedia.org/wiki/Center_of_mass]<br /> <br /> ==References==<br /> <br /> This section contains the the references you used while writing this page<br /> <br /> [[Category:Which Category did you place this in?]]</div>

Migitalex http://www.physicsbook.gatech.edu/index.php?title=File:Continuous_mass_COM_soln1.png&diff=7654 2015-12-02T04:07:09Z

<p>Migitalex: </p> <hr /> <div></div>

Migitalex http://www.physicsbook.gatech.edu/index.php?title=File:Continuous_mass_COM_2.png&diff=7649 2015-12-02T04:02:36Z

<p>Migitalex: </p> <hr /> <div></div>

Migitalex http://www.physicsbook.gatech.edu/index.php?title=Center_of_Mass&diff=7610 2015-12-02T03:41:09Z

<p>Migitalex: /* Examples */</p> <hr /> <div>Claimed by Alex Huynh (ahuynh9)<br /> <br /> ==The Main Idea==<br /> <br /> The center of mass of an object is the point in space where if a force was applied, the object moves according to Newton's laws without rotation. At the center of mass, the distribution of mass is balanced, and the average of the weighted position coordinates of the distributed mass defines its coordinates. Mechanical calculations are often simplified with respect to the center of mass of objects.<br /> <br /> [[File:Ahuynh5.png]]<br /> <br /> When a force is applied not to the center of mass:<br /> <br /> [[File:Ahuynh6.png]]<br /> ----<br /> <br /> ===A Mathematical Model===<br /> <br /> The position of the center of mass of an object can be found by summating the product of each point mass and its relative linear position and dividing by the sum by the total mass.<br /> <br /> [[File:Ahuynh3.png]]<br /> <br /> This equation can then be extended to three dimensions.<br /> <br /> [[File:Ahuynh1.gif]]<br /> <br /> When calculating the center of mass for a continuous distribution of mass, the expression becomes an infinite sum that can be expressed in the form of an integral.<br /> <br /> [[File:Ahuynh4.gif]]<br /> <br /> ----<br /> <br /> ==Examples==<br /> <br /> ===Simple===<br /> A 10 kg point mass and a 5 kg point mass are connected by a 10 m massless rod.<br /> <br /> [[File:1D_COM.png]]<br /> <br /> Find the center of mass. This is example of a 1-dimensional center of mass problem.<br /> <br /> ====Solution====<br /> First, we will need to establish an origin. For simplicity, we will establish the left end, the position of the 10 kg point mass, as the origin. Relative to the origin, the position of the 10 kg mass is 0 m and the position of the 5 kg mass is 10 m. Placing these values into our formula for 1-dimensional center of mass, we get:<br /> <br /> [[File:1D_COM_SOLN.png]]<br /> <br /> Therefore, the center of mass is 10/3 m from the left end of the rod. It is important to state your distances relative to your stated origin.<br /> <br /> ===Middling===<br /> 3 point masses are placed on the x-y plane as shown:<br /> <br /> [[File:2D_COM.png]]<br /> <br /> Find the center of mass. This is an example of a 2-dimensional center of mass problem.<br /> <br /> ====Solution====<br /> This problem is similar to the last problem except that we will need to find BOTH the x and y components of the center of mass. Like before, we need to establish an origin. For simplicity, we will establish the lower left corner, the position of the 3 kg mass as the origin. Then, we need to solve the two directions separately. We will start with the x direction. Relative to the origin, the 3 kg mass is at 0 m, the 8 kg mass is at 1 m, and the 4 kg mass is at 2 m. Placing these values into our center of mass of point masses formula, we get:<br /> <br /> [[File:2D_COM_SOLN1.png]]<br /> <br /> Therefore, the center of mass lies 16/15 m from the origin in the x direction.<br /> <br /> Next, we will solve for the y direction. Relative to the origin, the 3 kg mass is at 0 m, the 4 kg mass is at 1 m, and the 8 kg mass is at 2 m. Placing these values into our center of mass of point masses formula, we get:<br /> <br /> [[File:2D_COM_SOLN2.png]]<br /> <br /> Therefore, the center of mass lies 4/3 m from the origin in the y direction.<br /> <br /> The center of mass lies at the coordinates (16/15 m, 4/3 m).<br /> <br /> ===Difficult===<br /> <br /> ==Connectedness==<br /> #How is this topic connected to something that you are interested in?<br /> #How is it connected to your major?<br /> #Is there an interesting industrial application?<br /> <br /> ==History==<br /> <br /> The concept of center of mass was first introduced by Archimedes while he worked to simplify assumptions about gravity that amounted to a uniform field, thus arriving at the mathematical properties of the center of mass. In an experiment, Archimedes observed that the torque exerted on a lever by weights resting at various points along the lever is the same as what it would be if all of the weights were moved to a single point—their center of mass. He developed mathematical techniques for finding the centers of mass of objects of uniform density of various well-defined shapes.<br /> <br /> == See also ==<br /> <br /> Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?<br /> <br /> ===Further reading===<br /> <br /> PhysicsLab [http://dev.physicslab.org/document.aspx?doctype=3&amp;filename=rotarymotion_centermass.xml]<br /> <br /> HyperPhysics [http://hyperphysics.phy-astr.gsu.edu/hbase/cm.html]<br /> <br /> Wikipedia [https://en.wikipedia.org/wiki/Center_of_mass]<br /> <br /> ===External links===<br /> <br /> PhysicsLab [http://dev.physicslab.org/document.aspx?doctype=3&amp;filename=rotarymotion_centermass.xml]<br /> <br /> HyperPhysics [http://hyperphysics.phy-astr.gsu.edu/hbase/cm.html]<br /> <br /> Wikipedia [https://en.wikipedia.org/wiki/Center_of_mass]<br /> <br /> ==References==<br /> <br /> This section contains the the references you used while writing this page<br /> <br /> [[Category:Which Category did you place this in?]]</div>

Migitalex http://www.physicsbook.gatech.edu/index.php?title=File:2D_COM_SOLN2.png&diff=7603 2015-12-02T03:39:39Z

<p>Migitalex: </p> <hr /> <div></div>

Migitalex http://www.physicsbook.gatech.edu/index.php?title=File:2D_COM_SOLN1.png&diff=7599 2015-12-02T03:36:09Z

<p>Migitalex: </p> <hr /> <div></div>

Migitalex http://www.physicsbook.gatech.edu/index.php?title=File:2D_COM.png&diff=7578 2015-12-02T03:23:26Z

<p>Migitalex: </p> <hr /> <div></div>

Migitalex http://www.physicsbook.gatech.edu/index.php?title=Center_of_Mass&diff=7554 2015-12-02T03:11:21Z

<p>Migitalex: /* Examples */</p> <hr /> <div>Claimed by Alex Huynh (ahuynh9)<br /> <br /> ==The Main Idea==<br /> <br /> The center of mass of an object is the point in space where if a force was applied, the object moves according to Newton's laws without rotation. At the center of mass, the distribution of mass is balanced, and the average of the weighted position coordinates of the distributed mass defines its coordinates. Mechanical calculations are often simplified with respect to the center of mass of objects.<br /> <br /> [[File:Ahuynh5.png]]<br /> <br /> When a force is applied not to the center of mass:<br /> <br /> [[File:Ahuynh6.png]]<br /> ----<br /> <br /> ===A Mathematical Model===<br /> <br /> The position of the center of mass of an object can be found by summating the product of each point mass and its relative linear position and dividing by the sum by the total mass.<br /> <br /> [[File:Ahuynh3.png]]<br /> <br /> This equation can then be extended to three dimensions.<br /> <br /> [[File:Ahuynh1.gif]]<br /> <br /> When calculating the center of mass for a continuous distribution of mass, the expression becomes an infinite sum that can be expressed in the form of an integral.<br /> <br /> [[File:Ahuynh4.gif]]<br /> <br /> ----<br /> <br /> ==Examples==<br /> <br /> Be sure to show all steps in your solution and include diagrams whenever possible<br /> <br /> ===Simple===<br /> <br /> A 10 kg point mass and a 5 kg point mass are connected by a 10 m massless rod. Find the center of mass. This is example of a 1-dimensional center of mass problem.<br /> <br /> [[File:1D_COM.png]]<br /> <br /> ====Solution====<br /> First, we will need to establish an origin. For simplicity, we will establish the left end, the position of the 10 kg point mass, as the origin. Relative to the origin, the position of the 10 kg mass is 0 m and the position of the 5 kg mass is 10 m. Placing these values into our formula for 1-dimensional center of mass, we get:<br /> <br /> [[File:1D_COM_SOLN.png]]<br /> <br /> Therefore, the center of mass is 10/3 m from the left end of the rod. It is important to state your distances relative to your stated origin.<br /> <br /> ===Middling===<br /> ===Difficult===<br /> <br /> ==Connectedness==<br /> #How is this topic connected to something that you are interested in?<br /> #How is it connected to your major?<br /> #Is there an interesting industrial application?<br /> <br /> ==History==<br /> <br /> The concept of center of mass was first introduced by Archimedes while he worked to simplify assumptions about gravity that amounted to a uniform field, thus arriving at the mathematical properties of the center of mass. In an experiment, Archimedes observed that the torque exerted on a lever by weights resting at various points along the lever is the same as what it would be if all of the weights were moved to a single point—their center of mass. He developed mathematical techniques for finding the centers of mass of objects of uniform density of various well-defined shapes.<br /> <br /> == See also ==<br /> <br /> Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?<br /> <br /> ===Further reading===<br /> <br /> PhysicsLab [http://dev.physicslab.org/document.aspx?doctype=3&amp;filename=rotarymotion_centermass.xml]<br /> <br /> HyperPhysics [http://hyperphysics.phy-astr.gsu.edu/hbase/cm.html]<br /> <br /> Wikipedia [https://en.wikipedia.org/wiki/Center_of_mass]<br /> <br /> ===External links===<br /> <br /> PhysicsLab [http://dev.physicslab.org/document.aspx?doctype=3&amp;filename=rotarymotion_centermass.xml]<br /> <br /> HyperPhysics [http://hyperphysics.phy-astr.gsu.edu/hbase/cm.html]<br /> <br /> Wikipedia [https://en.wikipedia.org/wiki/Center_of_mass]<br /> <br /> ==References==<br /> <br /> This section contains the the references you used while writing this page<br /> <br /> [[Category:Which Category did you place this in?]]</div>

Migitalex http://www.physicsbook.gatech.edu/index.php?title=Center_of_Mass&diff=7551 2015-12-02T03:10:41Z

<p>Migitalex: /* Solution */</p> <hr /> <div>Claimed by Alex Huynh (ahuynh9)<br /> <br /> ==The Main Idea==<br /> <br /> The center of mass of an object is the point in space where if a force was applied, the object moves according to Newton's laws without rotation. At the center of mass, the distribution of mass is balanced, and the average of the weighted position coordinates of the distributed mass defines its coordinates. Mechanical calculations are often simplified with respect to the center of mass of objects.<br /> <br /> [[File:Ahuynh5.png]]<br /> <br /> When a force is applied not to the center of mass:<br /> <br /> [[File:Ahuynh6.png]]<br /> ----<br /> <br /> ===A Mathematical Model===<br /> <br /> The position of the center of mass of an object can be found by summating the product of each point mass and its relative linear position and dividing by the sum by the total mass.<br /> <br /> [[File:Ahuynh3.png]]<br /> <br /> This equation can then be extended to three dimensions.<br /> <br /> [[File:Ahuynh1.gif]]<br /> <br /> When calculating the center of mass for a continuous distribution of mass, the expression becomes an infinite sum that can be expressed in the form of an integral.<br /> <br /> [[File:Ahuynh4.gif]]<br /> <br /> ----<br /> <br /> ==Examples==<br /> <br /> Be sure to show all steps in your solution and include diagrams whenever possible<br /> <br /> ===Simple===<br /> <br /> A 10 kg point mass and a 5 kg point mass are connected by a 10 m massless rod. Find the center of mass. This is example of a 1-dimensional center of mass problem.<br /> [[File:1D_COM.png]]<br /> ====Solution====<br /> First, we will need to establish an origin. For simplicity, we will establish the left end, the position of the 10 kg point mass, as the origin. Relative to the origin, the position of the 10 kg mass is 0 m and the position of the 5 kg mass is 10 m. Placing these values into our formula for 1-dimensional center of mass, we get:<br /> [[File:1D_COM_SOLN.png]]<br /> Therefore, the center of mass is 10/3 m from the left end of the rod. It is important to state your distances relative to your stated origin.<br /> <br /> ===Middling===<br /> ===Difficult===<br /> <br /> ==Connectedness==<br /> #How is this topic connected to something that you are interested in?<br /> #How is it connected to your major?<br /> #Is there an interesting industrial application?<br /> <br /> ==History==<br /> <br /> The concept of center of mass was first introduced by Archimedes while he worked to simplify assumptions about gravity that amounted to a uniform field, thus arriving at the mathematical properties of the center of mass. In an experiment, Archimedes observed that the torque exerted on a lever by weights resting at various points along the lever is the same as what it would be if all of the weights were moved to a single point—their center of mass. He developed mathematical techniques for finding the centers of mass of objects of uniform density of various well-defined shapes.<br /> <br /> == See also ==<br /> <br /> Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?<br /> <br /> ===Further reading===<br /> <br /> PhysicsLab [http://dev.physicslab.org/document.aspx?doctype=3&amp;filename=rotarymotion_centermass.xml]<br /> <br /> HyperPhysics [http://hyperphysics.phy-astr.gsu.edu/hbase/cm.html]<br /> <br /> Wikipedia [https://en.wikipedia.org/wiki/Center_of_mass]<br /> <br /> ===External links===<br /> <br /> PhysicsLab [http://dev.physicslab.org/document.aspx?doctype=3&amp;filename=rotarymotion_centermass.xml]<br /> <br /> HyperPhysics [http://hyperphysics.phy-astr.gsu.edu/hbase/cm.html]<br /> <br /> Wikipedia [https://en.wikipedia.org/wiki/Center_of_mass]<br /> <br /> ==References==<br /> <br /> This section contains the the references you used while writing this page<br /> <br /> [[Category:Which Category did you place this in?]]</div>

Migitalex http://www.physicsbook.gatech.edu/index.php?title=Center_of_Mass&diff=7533 2015-12-02T03:04:14Z

<p>Migitalex: /* Solution */</p> <hr /> <div>Claimed by Alex Huynh (ahuynh9)<br /> <br /> ==The Main Idea==<br /> <br /> The center of mass of an object is the point in space where if a force was applied, the object moves according to Newton's laws without rotation. At the center of mass, the distribution of mass is balanced, and the average of the weighted position coordinates of the distributed mass defines its coordinates. Mechanical calculations are often simplified with respect to the center of mass of objects.<br /> <br /> [[File:Ahuynh5.png]]<br /> <br /> When a force is applied not to the center of mass:<br /> <br /> [[File:Ahuynh6.png]]<br /> ----<br /> <br /> ===A Mathematical Model===<br /> <br /> The position of the center of mass of an object can be found by summating the product of each point mass and its relative linear position and dividing by the sum by the total mass.<br /> <br /> [[File:Ahuynh3.png]]<br /> <br /> This equation can then be extended to three dimensions.<br /> <br /> [[File:Ahuynh1.gif]]<br /> <br /> When calculating the center of mass for a continuous distribution of mass, the expression becomes an infinite sum that can be expressed in the form of an integral.<br /> <br /> [[File:Ahuynh4.gif]]<br /> <br /> ----<br /> <br /> ==Examples==<br /> <br /> Be sure to show all steps in your solution and include diagrams whenever possible<br /> <br /> ===Simple===<br /> <br /> A 10 kg point mass and a 5 kg point mass are connected by a 10 m massless rod. Find the center of mass. This is example of a 1-dimensional center of mass problem.<br /> [[File:1D_COM.png]]<br /> ====Solution====<br /> First, we will need to establish an origin. For simplicity, we will establish the left end, the position of the 10 kg point mass, as the origin. Relative to the origin, the position of the 10 kg mass is 0 m and the position of the 5 kg mass is 10 m. Placing these values into our formula for 1-dimensional center of mass, we get:<br /> [[File:1D_COM_SOLN.png]]<br /> Therefore, the answer<br /> <br /> ===Middling===<br /> ===Difficult===<br /> <br /> ==Connectedness==<br /> #How is this topic connected to something that you are interested in?<br /> #How is it connected to your major?<br /> #Is there an interesting industrial application?<br /> <br /> ==History==<br /> <br /> The concept of center of mass was first introduced by Archimedes while he worked to simplify assumptions about gravity that amounted to a uniform field, thus arriving at the mathematical properties of the center of mass. In an experiment, Archimedes observed that the torque exerted on a lever by weights resting at various points along the lever is the same as what it would be if all of the weights were moved to a single point—their center of mass. He developed mathematical techniques for finding the centers of mass of objects of uniform density of various well-defined shapes.<br /> <br /> == See also ==<br /> <br /> Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?<br /> <br /> ===Further reading===<br /> <br /> PhysicsLab [http://dev.physicslab.org/document.aspx?doctype=3&amp;filename=rotarymotion_centermass.xml]<br /> <br /> HyperPhysics [http://hyperphysics.phy-astr.gsu.edu/hbase/cm.html]<br /> <br /> Wikipedia [https://en.wikipedia.org/wiki/Center_of_mass]<br /> <br /> ===External links===<br /> <br /> PhysicsLab [http://dev.physicslab.org/document.aspx?doctype=3&amp;filename=rotarymotion_centermass.xml]<br /> <br /> HyperPhysics [http://hyperphysics.phy-astr.gsu.edu/hbase/cm.html]<br /> <br /> Wikipedia [https://en.wikipedia.org/wiki/Center_of_mass]<br /> <br /> ==References==<br /> <br /> This section contains the the references you used while writing this page<br /> <br /> [[Category:Which Category did you place this in?]]</div>

Migitalex http://www.physicsbook.gatech.edu/index.php?title=Center_of_Mass&diff=7529 2015-12-02T03:02:40Z

<p>Migitalex: /* Solution */</p> <hr /> <div>Claimed by Alex Huynh (ahuynh9)<br /> <br /> ==The Main Idea==<br /> <br /> The center of mass of an object is the point in space where if a force was applied, the object moves according to Newton's laws without rotation. At the center of mass, the distribution of mass is balanced, and the average of the weighted position coordinates of the distributed mass defines its coordinates. Mechanical calculations are often simplified with respect to the center of mass of objects.<br /> <br /> [[File:Ahuynh5.png]]<br /> <br /> When a force is applied not to the center of mass:<br /> <br /> [[File:Ahuynh6.png]]<br /> ----<br /> <br /> ===A Mathematical Model===<br /> <br /> The position of the center of mass of an object can be found by summating the product of each point mass and its relative linear position and dividing by the sum by the total mass.<br /> <br /> [[File:Ahuynh3.png]]<br /> <br /> This equation can then be extended to three dimensions.<br /> <br /> [[File:Ahuynh1.gif]]<br /> <br /> When calculating the center of mass for a continuous distribution of mass, the expression becomes an infinite sum that can be expressed in the form of an integral.<br /> <br /> [[File:Ahuynh4.gif]]<br /> <br /> ----<br /> <br /> ==Examples==<br /> <br /> Be sure to show all steps in your solution and include diagrams whenever possible<br /> <br /> ===Simple===<br /> <br /> A 10 kg point mass and a 5 kg point mass are connected by a 10 m massless rod. Find the center of mass. This is example of a 1-dimensional center of mass problem.<br /> [[File:1D_COM.png]]<br /> ====Solution====<br /> First, we will need to establish an origin. For simplicity, we will establish the left end, the position of the 10 kg point mass, as the origin. Relative to the origin, the position of the 10 kg mass is 0 m and the position of the 5 kg mass is 10 m. Placing these values into our formula for 1-dimensional center of mass, we get:<br /> [[File:1D_COM_SOLN.png]]<br /> <br /> ===Middling===<br /> ===Difficult===<br /> <br /> ==Connectedness==<br /> #How is this topic connected to something that you are interested in?<br /> #How is it connected to your major?<br /> #Is there an interesting industrial application?<br /> <br /> ==History==<br /> <br /> The concept of center of mass was first introduced by Archimedes while he worked to simplify assumptions about gravity that amounted to a uniform field, thus arriving at the mathematical properties of the center of mass. In an experiment, Archimedes observed that the torque exerted on a lever by weights resting at various points along the lever is the same as what it would be if all of the weights were moved to a single point—their center of mass. He developed mathematical techniques for finding the centers of mass of objects of uniform density of various well-defined shapes.<br /> <br /> == See also ==<br /> <br /> Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?<br /> <br /> ===Further reading===<br /> <br /> PhysicsLab [http://dev.physicslab.org/document.aspx?doctype=3&amp;filename=rotarymotion_centermass.xml]<br /> <br /> HyperPhysics [http://hyperphysics.phy-astr.gsu.edu/hbase/cm.html]<br /> <br /> Wikipedia [https://en.wikipedia.org/wiki/Center_of_mass]<br /> <br /> ===External links===<br /> <br /> PhysicsLab [http://dev.physicslab.org/document.aspx?doctype=3&amp;filename=rotarymotion_centermass.xml]<br /> <br /> HyperPhysics [http://hyperphysics.phy-astr.gsu.edu/hbase/cm.html]<br /> <br /> Wikipedia [https://en.wikipedia.org/wiki/Center_of_mass]<br /> <br /> ==References==<br /> <br /> This section contains the the references you used while writing this page<br /> <br /> [[Category:Which Category did you place this in?]]</div>

Migitalex http://www.physicsbook.gatech.edu/index.php?title=File:1D_COM_SOLN.png&diff=7527 2015-12-02T03:02:33Z

<p>Migitalex: </p> <hr /> <div></div>

Migitalex http://www.physicsbook.gatech.edu/index.php?title=Center_of_Mass&diff=7504 2015-12-02T02:56:19Z

<p>Migitalex: /* Solution */</p> <hr /> <div>Claimed by Alex Huynh (ahuynh9)<br /> <br /> ==The Main Idea==<br /> <br /> The center of mass of an object is the point in space where if a force was applied, the object moves according to Newton's laws without rotation. At the center of mass, the distribution of mass is balanced, and the average of the weighted position coordinates of the distributed mass defines its coordinates. Mechanical calculations are often simplified with respect to the center of mass of objects.<br /> <br /> [[File:Ahuynh5.png]]<br /> <br /> When a force is applied not to the center of mass:<br /> <br /> [[File:Ahuynh6.png]]<br /> ----<br /> <br /> ===A Mathematical Model===<br /> <br /> The position of the center of mass of an object can be found by summating the product of each point mass and its relative linear position and dividing by the sum by the total mass.<br /> <br /> [[File:Ahuynh3.png]]<br /> <br /> This equation can then be extended to three dimensions.<br /> <br /> [[File:Ahuynh1.gif]]<br /> <br /> When calculating the center of mass for a continuous distribution of mass, the expression becomes an infinite sum that can be expressed in the form of an integral.<br /> <br /> [[File:Ahuynh4.gif]]<br /> <br /> ----<br /> <br /> ==Examples==<br /> <br /> Be sure to show all steps in your solution and include diagrams whenever possible<br /> <br /> ===Simple===<br /> <br /> A 10 kg point mass and a 5 kg point mass are connected by a 10 m massless rod. Find the center of mass. This is example of a 1-dimensional center of mass problem.<br /> [[File:1D_COM.png]]<br /> ====Solution====<br /> First, we will need to establish an origin. For simplicity, we will establish the left end, the position of the 10 kg point mass, as the origin. Relative to the origin, the position of the 10 kg mass is 0 m and the position of the 5 kg mass is 10 m. Placing these values into our formula for 1-dimensional center of mass, we get Xcm = [10 kg(0 m)+5 kg(10 m)]/(10 kg + 5 kg)<br /> <br /> ===Middling===<br /> ===Difficult===<br /> <br /> ==Connectedness==<br /> #How is this topic connected to something that you are interested in?<br /> #How is it connected to your major?<br /> #Is there an interesting industrial application?<br /> <br /> ==History==<br /> <br /> The concept of center of mass was first introduced by Archimedes while he worked to simplify assumptions about gravity that amounted to a uniform field, thus arriving at the mathematical properties of the center of mass. In an experiment, Archimedes observed that the torque exerted on a lever by weights resting at various points along the lever is the same as what it would be if all of the weights were moved to a single point—their center of mass. He developed mathematical techniques for finding the centers of mass of objects of uniform density of various well-defined shapes.<br /> <br /> == See also ==<br /> <br /> Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?<br /> <br /> ===Further reading===<br /> <br /> PhysicsLab [http://dev.physicslab.org/document.aspx?doctype=3&amp;filename=rotarymotion_centermass.xml]<br /> <br /> HyperPhysics [http://hyperphysics.phy-astr.gsu.edu/hbase/cm.html]<br /> <br /> Wikipedia [https://en.wikipedia.org/wiki/Center_of_mass]<br /> <br /> ===External links===<br /> <br /> PhysicsLab [http://dev.physicslab.org/document.aspx?doctype=3&amp;filename=rotarymotion_centermass.xml]<br /> <br /> HyperPhysics [http://hyperphysics.phy-astr.gsu.edu/hbase/cm.html]<br /> <br /> Wikipedia [https://en.wikipedia.org/wiki/Center_of_mass]<br /> <br /> ==References==<br /> <br /> This section contains the the references you used while writing this page<br /> <br /> [[Category:Which Category did you place this in?]]</div>

Migitalex http://www.physicsbook.gatech.edu/index.php?title=Center_of_Mass&diff=7492 2015-12-02T02:53:29Z

<p>Migitalex: /* The Main Idea */</p> <hr /> <div>Claimed by Alex Huynh (ahuynh9)<br /> <br /> ==The Main Idea==<br /> <br /> The center of mass of an object is the point in space where if a force was applied, the object moves according to Newton's laws without rotation. At the center of mass, the distribution of mass is balanced, and the average of the weighted position coordinates of the distributed mass defines its coordinates. Mechanical calculations are often simplified with respect to the center of mass of objects.<br /> <br /> [[File:Ahuynh5.png]]<br /> <br /> When a force is applied not to the center of mass:<br /> <br /> [[File:Ahuynh6.png]]<br /> ----<br /> <br /> ===A Mathematical Model===<br /> <br /> The position of the center of mass of an object can be found by summating the product of each point mass and its relative linear position and dividing by the sum by the total mass.<br /> <br /> [[File:Ahuynh3.png]]<br /> <br /> This equation can then be extended to three dimensions.<br /> <br /> [[File:Ahuynh1.gif]]<br /> <br /> When calculating the center of mass for a continuous distribution of mass, the expression becomes an infinite sum that can be expressed in the form of an integral.<br /> <br /> [[File:Ahuynh4.gif]]<br /> <br /> ----<br /> <br /> ==Examples==<br /> <br /> Be sure to show all steps in your solution and include diagrams whenever possible<br /> <br /> ===Simple===<br /> <br /> A 10 kg point mass and a 5 kg point mass are connected by a 10 m massless rod. Find the center of mass. This is example of a 1-dimensional center of mass problem.<br /> [[File:1D_COM.png]]<br /> ====Solution====<br /> First, we will<br /> <br /> ===Middling===<br /> ===Difficult===<br /> <br /> ==Connectedness==<br /> #How is this topic connected to something that you are interested in?<br /> #How is it connected to your major?<br /> #Is there an interesting industrial application?<br /> <br /> ==History==<br /> <br /> The concept of center of mass was first introduced by Archimedes while he worked to simplify assumptions about gravity that amounted to a uniform field, thus arriving at the mathematical properties of the center of mass. In an experiment, Archimedes observed that the torque exerted on a lever by weights resting at various points along the lever is the same as what it would be if all of the weights were moved to a single point—their center of mass. He developed mathematical techniques for finding the centers of mass of objects of uniform density of various well-defined shapes.<br /> <br /> == See also ==<br /> <br /> Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?<br /> <br /> ===Further reading===<br /> <br /> PhysicsLab [http://dev.physicslab.org/document.aspx?doctype=3&amp;filename=rotarymotion_centermass.xml]<br /> <br /> HyperPhysics [http://hyperphysics.phy-astr.gsu.edu/hbase/cm.html]<br /> <br /> Wikipedia [https://en.wikipedia.org/wiki/Center_of_mass]<br /> <br /> ===External links===<br /> <br /> PhysicsLab [http://dev.physicslab.org/document.aspx?doctype=3&amp;filename=rotarymotion_centermass.xml]<br /> <br /> HyperPhysics [http://hyperphysics.phy-astr.gsu.edu/hbase/cm.html]<br /> <br /> Wikipedia [https://en.wikipedia.org/wiki/Center_of_mass]<br /> <br /> ==References==<br /> <br /> This section contains the the references you used while writing this page<br /> <br /> [[Category:Which Category did you place this in?]]</div>

Migitalex http://www.physicsbook.gatech.edu/index.php?title=Center_of_Mass&diff=7474 2015-12-02T02:50:42Z

<p>Migitalex: /* Simple */</p> <hr /> <div>Claimed by Alex Huynh (ahuynh9)<br /> <br /> ==The Main Idea==<br /> <br /> The center of mass of an object is the point in space where if a force was applied, the object moves according to Newton's laws without rotation. At the center of mass, the distribution of mass is balanced, and the average of the weighted position coordinates of the distributed mass defines its coordinates. Mechanical calculations are often simplified with respect to the center of mass of objects.<br /> <br /> [[File:Ahuynh5.png]]<br /> <br /> When a force is not applied to the center of mass:<br /> <br /> [[File:Ahuynh6.png]]<br /> ----<br /> <br /> ===A Mathematical Model===<br /> <br /> The position of the center of mass of an object can be found by summating the product of each point mass and its relative linear position and dividing by the sum by the total mass.<br /> <br /> [[File:Ahuynh3.png]]<br /> <br /> This equation can then be extended to three dimensions.<br /> <br /> [[File:Ahuynh1.gif]]<br /> <br /> When calculating the center of mass for a continuous distribution of mass, the expression becomes an infinite sum that can be expressed in the form of an integral.<br /> <br /> [[File:Ahuynh4.gif]]<br /> <br /> ----<br /> <br /> ==Examples==<br /> <br /> Be sure to show all steps in your solution and include diagrams whenever possible<br /> <br /> ===Simple===<br /> <br /> A 10 kg point mass and a 5 kg point mass are connected by a 10 m massless rod. Find the center of mass. This is example of a 1-dimensional center of mass problem.<br /> [[File:1D_COM.png]]<br /> ====Solution====<br /> First, we will<br /> <br /> ===Middling===<br /> ===Difficult===<br /> <br /> ==Connectedness==<br /> #How is this topic connected to something that you are interested in?<br /> #How is it connected to your major?<br /> #Is there an interesting industrial application?<br /> <br /> ==History==<br /> <br /> The concept of center of mass was first introduced by Archimedes while he worked to simplify assumptions about gravity that amounted to a uniform field, thus arriving at the mathematical properties of the center of mass. In an experiment, Archimedes observed that the torque exerted on a lever by weights resting at various points along the lever is the same as what it would be if all of the weights were moved to a single point—their center of mass. He developed mathematical techniques for finding the centers of mass of objects of uniform density of various well-defined shapes.<br /> <br /> == See also ==<br /> <br /> Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?<br /> <br /> ===Further reading===<br /> <br /> PhysicsLab [http://dev.physicslab.org/document.aspx?doctype=3&amp;filename=rotarymotion_centermass.xml]<br /> <br /> HyperPhysics [http://hyperphysics.phy-astr.gsu.edu/hbase/cm.html]<br /> <br /> Wikipedia [https://en.wikipedia.org/wiki/Center_of_mass]<br /> <br /> ===External links===<br /> <br /> PhysicsLab [http://dev.physicslab.org/document.aspx?doctype=3&amp;filename=rotarymotion_centermass.xml]<br /> <br /> HyperPhysics [http://hyperphysics.phy-astr.gsu.edu/hbase/cm.html]<br /> <br /> Wikipedia [https://en.wikipedia.org/wiki/Center_of_mass]<br /> <br /> ==References==<br /> <br /> This section contains the the references you used while writing this page<br /> <br /> [[Category:Which Category did you place this in?]]</div>

Migitalex http://www.physicsbook.gatech.edu/index.php?title=Center_of_Mass&diff=7446 2015-12-02T02:45:09Z

<p>Migitalex: /* Simple */</p> <hr /> <div>Claimed by Alex Huynh (ahuynh9)<br /> <br /> ==The Main Idea==<br /> <br /> The center of mass of an object is the point in space where if a force was applied, the object moves according to Newton's laws without rotation. At the center of mass, the distribution of mass is balanced, and the average of the weighted position coordinates of the distributed mass defines its coordinates. Mechanical calculations are often simplified with respect to the center of mass of objects.<br /> <br /> [[File:Ahuynh5.png]]<br /> <br /> When a force is not applied to the center of mass:<br /> <br /> [[File:Ahuynh6.png]]<br /> ----<br /> <br /> ===A Mathematical Model===<br /> <br /> The position of the center of mass of an object can be found by summating the product of each point mass and its relative linear position and dividing by the sum by the total mass.<br /> <br /> [[File:Ahuynh3.png]]<br /> <br /> This equation can then be extended to three dimensions.<br /> <br /> [[File:Ahuynh1.gif]]<br /> <br /> When calculating the center of mass for a continuous distribution of mass, the expression becomes an infinite sum that can be expressed in the form of an integral.<br /> <br /> [[File:Ahuynh4.gif]]<br /> <br /> ----<br /> <br /> ==Examples==<br /> <br /> Be sure to show all steps in your solution and include diagrams whenever possible<br /> <br /> ===Simple===<br /> [[File:1D_COM.png]]<br /> <br /> ===Middling===<br /> ===Difficult===<br /> <br /> ==Connectedness==<br /> #How is this topic connected to something that you are interested in?<br /> #How is it connected to your major?<br /> #Is there an interesting industrial application?<br /> <br /> ==History==<br /> <br /> The concept of center of mass was first introduced by Archimedes while he worked to simplify assumptions about gravity that amounted to a uniform field, thus arriving at the mathematical properties of the center of mass. In an experiment, Archimedes observed that the torque exerted on a lever by weights resting at various points along the lever is the same as what it would be if all of the weights were moved to a single point—their center of mass. He developed mathematical techniques for finding the centers of mass of objects of uniform density of various well-defined shapes.<br /> <br /> == See also ==<br /> <br /> Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?<br /> <br /> ===Further reading===<br /> <br /> PhysicsLab [http://dev.physicslab.org/document.aspx?doctype=3&amp;filename=rotarymotion_centermass.xml]<br /> <br /> HyperPhysics [http://hyperphysics.phy-astr.gsu.edu/hbase/cm.html]<br /> <br /> Wikipedia [https://en.wikipedia.org/wiki/Center_of_mass]<br /> <br /> ===External links===<br /> <br /> PhysicsLab [http://dev.physicslab.org/document.aspx?doctype=3&amp;filename=rotarymotion_centermass.xml]<br /> <br /> HyperPhysics [http://hyperphysics.phy-astr.gsu.edu/hbase/cm.html]<br /> <br /> Wikipedia [https://en.wikipedia.org/wiki/Center_of_mass]<br /> <br /> ==References==<br /> <br /> This section contains the the references you used while writing this page<br /> <br /> [[Category:Which Category did you place this in?]]</div>

Migitalex http://www.physicsbook.gatech.edu/index.php?title=File:1D_COM.png&diff=7442 2015-12-02T02:44:52Z

<p>Migitalex: </p> <hr /> <div></div>

Migitalex http://www.physicsbook.gatech.edu/index.php?title=Center_of_Mass&diff=7362 2015-12-02T02:24:16Z

<p>Migitalex: /* See also */</p> <hr /> <div>Claimed by Alex Huynh (ahuynh9)<br /> <br /> ==The Main Idea==<br /> <br /> The center of mass of an object is the point in space where if a force was applied, the object moves according to Newton's laws without rotation. At the center of mass, the distribution of mass is balanced, and the average of the weighted position coordinates of the distributed mass defines its coordinates. Mechanical calculations are often simplified with respect to the center of mass of objects.<br /> <br /> [[File:Ahuynh5.png]]<br /> <br /> When a force is not applied to the center of mass:<br /> <br /> [[File:Ahuynh6.png]]<br /> ----<br /> <br /> ===A Mathematical Model===<br /> <br /> The position of the center of mass of an object can be found by summating the product of each point mass and its relative linear position and dividing by the sum by the total mass.<br /> <br /> [[File:Ahuynh3.png]]<br /> <br /> This equation can then be extended to three dimensions.<br /> <br /> [[File:Ahuynh1.gif]]<br /> <br /> When calculating the center of mass for a continuous distribution of mass, the expression becomes an infinite sum that can be expressed in the form of an integral.<br /> <br /> [[File:Ahuynh4.gif]]<br /> <br /> ----<br /> <br /> ==Examples==<br /> <br /> Be sure to show all steps in your solution and include diagrams whenever possible<br /> <br /> ===Simple===<br /> ===Middling===<br /> ===Difficult===<br /> <br /> ==Connectedness==<br /> #How is this topic connected to something that you are interested in?<br /> #How is it connected to your major?<br /> #Is there an interesting industrial application?<br /> <br /> ==History==<br /> <br /> The concept of center of mass was first introduced by Archimedes while he worked to simplify assumptions about gravity that amounted to a uniform field, thus arriving at the mathematical properties of the center of mass. In an experiment, Archimedes observed that the torque exerted on a lever by weights resting at various points along the lever is the same as what it would be if all of the weights were moved to a single point—their center of mass. He developed mathematical techniques for finding the centers of mass of objects of uniform density of various well-defined shapes.<br /> <br /> == See also ==<br /> <br /> Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?<br /> <br /> ===Further reading===<br /> <br /> PhysicsLab [http://dev.physicslab.org/document.aspx?doctype=3&amp;filename=rotarymotion_centermass.xml]<br /> <br /> HyperPhysics [http://hyperphysics.phy-astr.gsu.edu/hbase/cm.html]<br /> <br /> Wikipedia [https://en.wikipedia.org/wiki/Center_of_mass]<br /> <br /> ===External links===<br /> <br /> PhysicsLab [http://dev.physicslab.org/document.aspx?doctype=3&amp;filename=rotarymotion_centermass.xml]<br /> <br /> HyperPhysics [http://hyperphysics.phy-astr.gsu.edu/hbase/cm.html]<br /> <br /> Wikipedia [https://en.wikipedia.org/wiki/Center_of_mass]<br /> <br /> ==References==<br /> <br /> This section contains the the references you used while writing this page<br /> <br /> [[Category:Which Category did you place this in?]]</div>

Migitalex http://www.physicsbook.gatech.edu/index.php?title=Center_of_Mass&diff=7356 2015-12-02T02:22:45Z

<p>Migitalex: /* The Main Idea */</p> <hr /> <div>Claimed by Alex Huynh (ahuynh9)<br /> <br /> ==The Main Idea==<br /> <br /> The center of mass of an object is the point in space where if a force was applied, the object moves according to Newton's laws without rotation. At the center of mass, the distribution of mass is balanced, and the average of the weighted position coordinates of the distributed mass defines its coordinates. Mechanical calculations are often simplified with respect to the center of mass of objects.<br /> <br /> [[File:Ahuynh5.png]]<br /> <br /> When a force is not applied to the center of mass:<br /> <br /> [[File:Ahuynh6.png]]<br /> ----<br /> <br /> ===A Mathematical Model===<br /> <br /> The position of the center of mass of an object can be found by summating the product of each point mass and its relative linear position and dividing by the sum by the total mass.<br /> <br /> [[File:Ahuynh3.png]]<br /> <br /> This equation can then be extended to three dimensions.<br /> <br /> [[File:Ahuynh1.gif]]<br /> <br /> When calculating the center of mass for a continuous distribution of mass, the expression becomes an infinite sum that can be expressed in the form of an integral.<br /> <br /> [[File:Ahuynh4.gif]]<br /> <br /> ----<br /> <br /> ==Examples==<br /> <br /> Be sure to show all steps in your solution and include diagrams whenever possible<br /> <br /> ===Simple===<br /> ===Middling===<br /> ===Difficult===<br /> <br /> ==Connectedness==<br /> #How is this topic connected to something that you are interested in?<br /> #How is it connected to your major?<br /> #Is there an interesting industrial application?<br /> <br /> ==History==<br /> <br /> The concept of center of mass was first introduced by Archimedes while he worked to simplify assumptions about gravity that amounted to a uniform field, thus arriving at the mathematical properties of the center of mass. In an experiment, Archimedes observed that the torque exerted on a lever by weights resting at various points along the lever is the same as what it would be if all of the weights were moved to a single point—their center of mass. He developed mathematical techniques for finding the centers of mass of objects of uniform density of various well-defined shapes.<br /> <br /> == See also ==<br /> <br /> Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?<br /> <br /> ===Further reading===<br /> <br /> Books, Articles or other print media on this topic<br /> <br /> ===External links===<br /> <br /> PhysicsLab [http://dev.physicslab.org/document.aspx?doctype=3&amp;filename=rotarymotion_centermass.xml]<br /> <br /> HyperPhysics [http://hyperphysics.phy-astr.gsu.edu/hbase/cm.html]<br /> <br /> Wikipedia [https://en.wikipedia.org/wiki/Center_of_mass]<br /> <br /> ==References==<br /> <br /> This section contains the the references you used while writing this page<br /> <br /> [[Category:Which Category did you place this in?]]</div>

Migitalex http://www.physicsbook.gatech.edu/index.php?title=Center_of_Mass&diff=7355 2015-12-02T02:22:22Z

<p>Migitalex: /* The Main Idea */</p> <hr /> <div>Claimed by Alex Huynh (ahuynh9)<br /> <br /> ==The Main Idea==<br /> <br /> The center of mass of an object is the point in space where if a force was applied, the object moves according to Newton's laws without rotation. At the center of mass, the distribution of mass is balanced, and the average of the weighted position coordinates of the distributed mass defines its coordinates. Mechanical calculations are often simplified with respect to the center of mass of objects.<br /> <br /> [[File:Ahuynh5.png]]<br /> <br /> When a force is not applied to the center of mass:<br /> <br /> [[File:Ahuynh6]]<br /> ----<br /> <br /> ===A Mathematical Model===<br /> <br /> The position of the center of mass of an object can be found by summating the product of each point mass and its relative linear position and dividing by the sum by the total mass.<br /> <br /> [[File:Ahuynh3.png]]<br /> <br /> This equation can then be extended to three dimensions.<br /> <br /> [[File:Ahuynh1.gif]]<br /> <br /> When calculating the center of mass for a continuous distribution of mass, the expression becomes an infinite sum that can be expressed in the form of an integral.<br /> <br /> [[File:Ahuynh4.gif]]<br /> <br /> ----<br /> <br /> ==Examples==<br /> <br /> Be sure to show all steps in your solution and include diagrams whenever possible<br /> <br /> ===Simple===<br /> ===Middling===<br /> ===Difficult===<br /> <br /> ==Connectedness==<br /> #How is this topic connected to something that you are interested in?<br /> #How is it connected to your major?<br /> #Is there an interesting industrial application?<br /> <br /> ==History==<br /> <br /> The concept of center of mass was first introduced by Archimedes while he worked to simplify assumptions about gravity that amounted to a uniform field, thus arriving at the mathematical properties of the center of mass. In an experiment, Archimedes observed that the torque exerted on a lever by weights resting at various points along the lever is the same as what it would be if all of the weights were moved to a single point—their center of mass. He developed mathematical techniques for finding the centers of mass of objects of uniform density of various well-defined shapes.<br /> <br /> == See also ==<br /> <br /> Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?<br /> <br /> ===Further reading===<br /> <br /> Books, Articles or other print media on this topic<br /> <br /> ===External links===<br /> <br /> PhysicsLab [http://dev.physicslab.org/document.aspx?doctype=3&amp;filename=rotarymotion_centermass.xml]<br /> <br /> HyperPhysics [http://hyperphysics.phy-astr.gsu.edu/hbase/cm.html]<br /> <br /> Wikipedia [https://en.wikipedia.org/wiki/Center_of_mass]<br /> <br /> ==References==<br /> <br /> This section contains the the references you used while writing this page<br /> <br /> [[Category:Which Category did you place this in?]]</div>

Migitalex http://www.physicsbook.gatech.edu/index.php?title=File:Ahuynh6.png&diff=7353 2015-12-02T02:21:37Z

<p>Migitalex: </p> <hr /> <div></div>

Migitalex http://www.physicsbook.gatech.edu/index.php?title=Center_of_Mass&diff=7348 2015-12-02T02:20:12Z

<p>Migitalex: /* External links */</p> <hr /> <div>Claimed by Alex Huynh (ahuynh9)<br /> <br /> ==The Main Idea==<br /> <br /> The center of mass of an object is the point in space where if a force was applied, the object moves according to Newton's laws without rotation. At the center of mass, the distribution of mass is balanced, and the average of the weighted position coordinates of the distributed mass defines its coordinates. Mechanical calculations are often simplified with respect to the center of mass of objects.<br /> <br /> [[File:Ahuynh5.png]]<br /> ----<br /> <br /> ===A Mathematical Model===<br /> <br /> The position of the center of mass of an object can be found by summating the product of each point mass and its relative linear position and dividing by the sum by the total mass.<br /> <br /> [[File:Ahuynh3.png]]<br /> <br /> This equation can then be extended to three dimensions.<br /> <br /> [[File:Ahuynh1.gif]]<br /> <br /> When calculating the center of mass for a continuous distribution of mass, the expression becomes an infinite sum that can be expressed in the form of an integral.<br /> <br /> [[File:Ahuynh4.gif]]<br /> <br /> ----<br /> <br /> ==Examples==<br /> <br /> Be sure to show all steps in your solution and include diagrams whenever possible<br /> <br /> ===Simple===<br /> ===Middling===<br /> ===Difficult===<br /> <br /> ==Connectedness==<br /> #How is this topic connected to something that you are interested in?<br /> #How is it connected to your major?<br /> #Is there an interesting industrial application?<br /> <br /> ==History==<br /> <br /> The concept of center of mass was first introduced by Archimedes while he worked to simplify assumptions about gravity that amounted to a uniform field, thus arriving at the mathematical properties of the center of mass. In an experiment, Archimedes observed that the torque exerted on a lever by weights resting at various points along the lever is the same as what it would be if all of the weights were moved to a single point—their center of mass. He developed mathematical techniques for finding the centers of mass of objects of uniform density of various well-defined shapes.<br /> <br /> == See also ==<br /> <br /> Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?<br /> <br /> ===Further reading===<br /> <br /> Books, Articles or other print media on this topic<br /> <br /> ===External links===<br /> <br /> PhysicsLab [http://dev.physicslab.org/document.aspx?doctype=3&amp;filename=rotarymotion_centermass.xml]<br /> <br /> HyperPhysics [http://hyperphysics.phy-astr.gsu.edu/hbase/cm.html]<br /> <br /> Wikipedia [https://en.wikipedia.org/wiki/Center_of_mass]<br /> <br /> ==References==<br /> <br /> This section contains the the references you used while writing this page<br /> <br /> [[Category:Which Category did you place this in?]]</div>

Migitalex http://www.physicsbook.gatech.edu/index.php?title=Center_of_Mass&diff=7342 2015-12-02T02:18:35Z

<p>Migitalex: /* External links */</p> <hr /> <div>Claimed by Alex Huynh (ahuynh9)<br /> <br /> ==The Main Idea==<br /> <br /> The center of mass of an object is the point in space where if a force was applied, the object moves according to Newton's laws without rotation. At the center of mass, the distribution of mass is balanced, and the average of the weighted position coordinates of the distributed mass defines its coordinates. Mechanical calculations are often simplified with respect to the center of mass of objects.<br /> <br /> [[File:Ahuynh5.png]]<br /> ----<br /> <br /> ===A Mathematical Model===<br /> <br /> The position of the center of mass of an object can be found by summating the product of each point mass and its relative linear position and dividing by the sum by the total mass.<br /> <br /> [[File:Ahuynh3.png]]<br /> <br /> This equation can then be extended to three dimensions.<br /> <br /> [[File:Ahuynh1.gif]]<br /> <br /> When calculating the center of mass for a continuous distribution of mass, the expression becomes an infinite sum that can be expressed in the form of an integral.<br /> <br /> [[File:Ahuynh4.gif]]<br /> <br /> ----<br /> <br /> ==Examples==<br /> <br /> Be sure to show all steps in your solution and include diagrams whenever possible<br /> <br /> ===Simple===<br /> ===Middling===<br /> ===Difficult===<br /> <br /> ==Connectedness==<br /> #How is this topic connected to something that you are interested in?<br /> #How is it connected to your major?<br /> #Is there an interesting industrial application?<br /> <br /> ==History==<br /> <br /> The concept of center of mass was first introduced by Archimedes while he worked to simplify assumptions about gravity that amounted to a uniform field, thus arriving at the mathematical properties of the center of mass. In an experiment, Archimedes observed that the torque exerted on a lever by weights resting at various points along the lever is the same as what it would be if all of the weights were moved to a single point—their center of mass. He developed mathematical techniques for finding the centers of mass of objects of uniform density of various well-defined shapes.<br /> <br /> == See also ==<br /> <br /> Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?<br /> <br /> ===Further reading===<br /> <br /> Books, Articles or other print media on this topic<br /> <br /> ===External links===<br /> <br /> Physicslab [http://dev.physicslab.org/document.aspx?doctype=3&amp;filename=rotarymotion_centermass.xml]<br /> <br /> [http://hyperphysics.phy-astr.gsu.edu/hbase/cm.html]<br /> <br /> [https://en.wikipedia.org/wiki/Center_of_mass]<br /> <br /> ==References==<br /> <br /> This section contains the the references you used while writing this page<br /> <br /> [[Category:Which Category did you place this in?]]</div>

Migitalex http://www.physicsbook.gatech.edu/index.php?title=Center_of_Mass&diff=7341 2015-12-02T02:18:14Z

<p>Migitalex: /* External links */</p> <hr /> <div>Claimed by Alex Huynh (ahuynh9)<br /> <br /> ==The Main Idea==<br /> <br /> The center of mass of an object is the point in space where if a force was applied, the object moves according to Newton's laws without rotation. At the center of mass, the distribution of mass is balanced, and the average of the weighted position coordinates of the distributed mass defines its coordinates. Mechanical calculations are often simplified with respect to the center of mass of objects.<br /> <br /> [[File:Ahuynh5.png]]<br /> ----<br /> <br /> ===A Mathematical Model===<br /> <br /> The position of the center of mass of an object can be found by summating the product of each point mass and its relative linear position and dividing by the sum by the total mass.<br /> <br /> [[File:Ahuynh3.png]]<br /> <br /> This equation can then be extended to three dimensions.<br /> <br /> [[File:Ahuynh1.gif]]<br /> <br /> When calculating the center of mass for a continuous distribution of mass, the expression becomes an infinite sum that can be expressed in the form of an integral.<br /> <br /> [[File:Ahuynh4.gif]]<br /> <br /> ----<br /> <br /> ==Examples==<br /> <br /> Be sure to show all steps in your solution and include diagrams whenever possible<br /> <br /> ===Simple===<br /> ===Middling===<br /> ===Difficult===<br /> <br /> ==Connectedness==<br /> #How is this topic connected to something that you are interested in?<br /> #How is it connected to your major?<br /> #Is there an interesting industrial application?<br /> <br /> ==History==<br /> <br /> The concept of center of mass was first introduced by Archimedes while he worked to simplify assumptions about gravity that amounted to a uniform field, thus arriving at the mathematical properties of the center of mass. In an experiment, Archimedes observed that the torque exerted on a lever by weights resting at various points along the lever is the same as what it would be if all of the weights were moved to a single point—their center of mass. He developed mathematical techniques for finding the centers of mass of objects of uniform density of various well-defined shapes.<br /> <br /> == See also ==<br /> <br /> Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?<br /> <br /> ===Further reading===<br /> <br /> Books, Articles or other print media on this topic<br /> <br /> ===External links===<br /> <br /> [http://dev.physicslab.org/document.aspx?doctype=3&amp;filename=rotarymotion_centermass.xml]<br /> <br /> [http://hyperphysics.phy-astr.gsu.edu/hbase/cm.html]<br /> <br /> [https://en.wikipedia.org/wiki/Center_of_mass]<br /> <br /> ==References==<br /> <br /> This section contains the the references you used while writing this page<br /> <br /> [[Category:Which Category did you place this in?]]</div>

Migitalex http://www.physicsbook.gatech.edu/index.php?title=Center_of_Mass&diff=7340 2015-12-02T02:17:47Z

<p>Migitalex: /* External links */</p> <hr /> <div>Claimed by Alex Huynh (ahuynh9)<br /> <br /> ==The Main Idea==<br /> <br /> The center of mass of an object is the point in space where if a force was applied, the object moves according to Newton's laws without rotation. At the center of mass, the distribution of mass is balanced, and the average of the weighted position coordinates of the distributed mass defines its coordinates. Mechanical calculations are often simplified with respect to the center of mass of objects.<br /> <br /> [[File:Ahuynh5.png]]<br /> ----<br /> <br /> ===A Mathematical Model===<br /> <br /> The position of the center of mass of an object can be found by summating the product of each point mass and its relative linear position and dividing by the sum by the total mass.<br /> <br /> [[File:Ahuynh3.png]]<br /> <br /> This equation can then be extended to three dimensions.<br /> <br /> [[File:Ahuynh1.gif]]<br /> <br /> When calculating the center of mass for a continuous distribution of mass, the expression becomes an infinite sum that can be expressed in the form of an integral.<br /> <br /> [[File:Ahuynh4.gif]]<br /> <br /> ----<br /> <br /> ==Examples==<br /> <br /> Be sure to show all steps in your solution and include diagrams whenever possible<br /> <br /> ===Simple===<br /> ===Middling===<br /> ===Difficult===<br /> <br /> ==Connectedness==<br /> #How is this topic connected to something that you are interested in?<br /> #How is it connected to your major?<br /> #Is there an interesting industrial application?<br /> <br /> ==History==<br /> <br /> The concept of center of mass was first introduced by Archimedes while he worked to simplify assumptions about gravity that amounted to a uniform field, thus arriving at the mathematical properties of the center of mass. In an experiment, Archimedes observed that the torque exerted on a lever by weights resting at various points along the lever is the same as what it would be if all of the weights were moved to a single point—their center of mass. He developed mathematical techniques for finding the centers of mass of objects of uniform density of various well-defined shapes.<br /> <br /> == See also ==<br /> <br /> Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?<br /> <br /> ===Further reading===<br /> <br /> Books, Articles or other print media on this topic<br /> <br /> ===External links===<br /> <br /> [[[http://dev.physicslab.org/document.aspx?doctype=3&amp;filename=rotarymotion_centermass.xml]]]<br /> <br /> [http://hyperphysics.phy-astr.gsu.edu/hbase/cm.html]<br /> <br /> [https://en.wikipedia.org/wiki/Center_of_mass]<br /> <br /> ==References==<br /> <br /> This section contains the the references you used while writing this page<br /> <br /> [[Category:Which Category did you place this in?]]</div>

Migitalex http://www.physicsbook.gatech.edu/index.php?title=Center_of_Mass&diff=7339 2015-12-02T02:17:15Z

<p>Migitalex: /* External links */</p> <hr /> <div>Claimed by Alex Huynh (ahuynh9)<br /> <br /> ==The Main Idea==<br /> <br /> The center of mass of an object is the point in space where if a force was applied, the object moves according to Newton's laws without rotation. At the center of mass, the distribution of mass is balanced, and the average of the weighted position coordinates of the distributed mass defines its coordinates. Mechanical calculations are often simplified with respect to the center of mass of objects.<br /> <br /> [[File:Ahuynh5.png]]<br /> ----<br /> <br /> ===A Mathematical Model===<br /> <br /> The position of the center of mass of an object can be found by summating the product of each point mass and its relative linear position and dividing by the sum by the total mass.<br /> <br /> [[File:Ahuynh3.png]]<br /> <br /> This equation can then be extended to three dimensions.<br /> <br /> [[File:Ahuynh1.gif]]<br /> <br /> When calculating the center of mass for a continuous distribution of mass, the expression becomes an infinite sum that can be expressed in the form of an integral.<br /> <br /> [[File:Ahuynh4.gif]]<br /> <br /> ----<br /> <br /> ==Examples==<br /> <br /> Be sure to show all steps in your solution and include diagrams whenever possible<br /> <br /> ===Simple===<br /> ===Middling===<br /> ===Difficult===<br /> <br /> ==Connectedness==<br /> #How is this topic connected to something that you are interested in?<br /> #How is it connected to your major?<br /> #Is there an interesting industrial application?<br /> <br /> ==History==<br /> <br /> The concept of center of mass was first introduced by Archimedes while he worked to simplify assumptions about gravity that amounted to a uniform field, thus arriving at the mathematical properties of the center of mass. In an experiment, Archimedes observed that the torque exerted on a lever by weights resting at various points along the lever is the same as what it would be if all of the weights were moved to a single point—their center of mass. He developed mathematical techniques for finding the centers of mass of objects of uniform density of various well-defined shapes.<br /> <br /> == See also ==<br /> <br /> Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?<br /> <br /> ===Further reading===<br /> <br /> Books, Articles or other print media on this topic<br /> <br /> ===External links===<br /> <br /> [[http://dev.physicslab.org/document.aspx?doctype=3&amp;filename=rotarymotion_centermass.xml]]<br /> <br /> [http://dev.physicslab.org/document.aspx?doctype=3&amp;filename=rotarymotion_centermass.xml]<br /> <br /> [http://hyperphysics.phy-astr.gsu.edu/hbase/cm.html]<br /> <br /> [https://en.wikipedia.org/wiki/Center_of_mass]<br /> <br /> ==References==<br /> <br /> This section contains the the references you used while writing this page<br /> <br /> [[Category:Which Category did you place this in?]]</div>

Migitalex http://www.physicsbook.gatech.edu/index.php?title=Center_of_Mass&diff=6811 2015-12-01T22:47:02Z

<p>Migitalex: /* External links */</p> <hr /> <div>Claimed by Alex Huynh (ahuynh9)<br /> <br /> ==The Main Idea==<br /> <br /> The center of mass of an object is the point in space where if a force was applied, the object moves according to Newton's laws without rotation. At the center of mass, the distribution of mass is balanced, and the average of the weighted position coordinates of the distributed mass defines its coordinates. Mechanical calculations are often simplified with respect to the center of mass of objects.<br /> <br /> [[File:Ahuynh5.png]]<br /> ----<br /> <br /> ===A Mathematical Model===<br /> <br /> The position of the center of mass of an object can be found by summating the product of each point mass and its relative linear position and dividing by the sum by the total mass.<br /> <br /> [[File:Ahuynh3.png]]<br /> <br /> This equation can then be extended to three dimensions.<br /> <br /> [[File:Ahuynh1.gif]]<br /> <br /> When calculating the center of mass for a continuous distribution of mass, the expression becomes an infinite sum that can be expressed in the form of an integral.<br /> <br /> [[File:Ahuynh4.gif]]<br /> <br /> ----<br /> <br /> ==Examples==<br /> <br /> Be sure to show all steps in your solution and include diagrams whenever possible<br /> <br /> ===Simple===<br /> ===Middling===<br /> ===Difficult===<br /> <br /> ==Connectedness==<br /> #How is this topic connected to something that you are interested in?<br /> #How is it connected to your major?<br /> #Is there an interesting industrial application?<br /> <br /> ==History==<br /> <br /> The concept of center of mass was first introduced by Archimedes while he worked to simplify assumptions about gravity that amounted to a uniform field, thus arriving at the mathematical properties of the center of mass. In an experiment, Archimedes observed that the torque exerted on a lever by weights resting at various points along the lever is the same as what it would be if all of the weights were moved to a single point—their center of mass. He developed mathematical techniques for finding the centers of mass of objects of uniform density of various well-defined shapes.<br /> <br /> == See also ==<br /> <br /> Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?<br /> <br /> ===Further reading===<br /> <br /> Books, Articles or other print media on this topic<br /> <br /> ===External links===<br /> <br /> [http://dev.physicslab.org/document.aspx?doctype=3&amp;filename=rotarymotion_centermass.xml]<br /> <br /> [http://hyperphysics.phy-astr.gsu.edu/hbase/cm.html]<br /> <br /> [https://en.wikipedia.org/wiki/Center_of_mass]<br /> <br /> ==References==<br /> <br /> This section contains the the references you used while writing this page<br /> <br /> [[Category:Which Category did you place this in?]]</div>

Migitalex http://www.physicsbook.gatech.edu/index.php?title=Center_of_Mass&diff=6796 2015-12-01T22:41:05Z

<p>Migitalex: /* History */</p> <hr /> <div>Claimed by Alex Huynh (ahuynh9)<br /> <br /> ==The Main Idea==<br /> <br /> The center of mass of an object is the point in space where if a force was applied, the object moves according to Newton's laws without rotation. At the center of mass, the distribution of mass is balanced, and the average of the weighted position coordinates of the distributed mass defines its coordinates. Mechanical calculations are often simplified with respect to the center of mass of objects.<br /> <br /> [[File:Ahuynh5.png]]<br /> ----<br /> <br /> ===A Mathematical Model===<br /> <br /> The position of the center of mass of an object can be found by summating the product of each point mass and its relative linear position and dividing by the sum by the total mass.<br /> <br /> [[File:Ahuynh3.png]]<br /> <br /> This equation can then be extended to three dimensions.<br /> <br /> [[File:Ahuynh1.gif]]<br /> <br /> When calculating the center of mass for a continuous distribution of mass, the expression becomes an infinite sum that can be expressed in the form of an integral.<br /> <br /> [[File:Ahuynh4.gif]]<br /> <br /> ----<br /> <br /> ==Examples==<br /> <br /> Be sure to show all steps in your solution and include diagrams whenever possible<br /> <br /> ===Simple===<br /> ===Middling===<br /> ===Difficult===<br /> <br /> ==Connectedness==<br /> #How is this topic connected to something that you are interested in?<br /> #How is it connected to your major?<br /> #Is there an interesting industrial application?<br /> <br /> ==History==<br /> <br /> The concept of center of mass was first introduced by Archimedes while he worked to simplify assumptions about gravity that amounted to a uniform field, thus arriving at the mathematical properties of the center of mass. In an experiment, Archimedes observed that the torque exerted on a lever by weights resting at various points along the lever is the same as what it would be if all of the weights were moved to a single point—their center of mass. He developed mathematical techniques for finding the centers of mass of objects of uniform density of various well-defined shapes.<br /> <br /> == See also ==<br /> <br /> Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?<br /> <br /> ===Further reading===<br /> <br /> Books, Articles or other print media on this topic<br /> <br /> ===External links===<br /> <br /> Internet resources on this topic<br /> <br /> ==References==<br /> <br /> This section contains the the references you used while writing this page<br /> <br /> [[Category:Which Category did you place this in?]]</div>

Migitalex http://www.physicsbook.gatech.edu/index.php?title=Center_of_Mass&diff=6774 2015-12-01T22:31:19Z

<p>Migitalex: /* A Mathematical Model */</p> <hr /> <div>Claimed by Alex Huynh (ahuynh9)<br /> <br /> ==The Main Idea==<br /> <br /> The center of mass of an object is the point in space where if a force was applied, the object moves according to Newton's laws without rotation. At the center of mass, the distribution of mass is balanced, and the average of the weighted position coordinates of the distributed mass defines its coordinates. Mechanical calculations are often simplified with respect to the center of mass of objects.<br /> <br /> [[File:Ahuynh5.png]]<br /> ----<br /> <br /> ===A Mathematical Model===<br /> <br /> The position of the center of mass of an object can be found by summating the product of each point mass and its relative linear position and dividing by the sum by the total mass.<br /> <br /> [[File:Ahuynh3.png]]<br /> <br /> This equation can then be extended to three dimensions.<br /> <br /> [[File:Ahuynh1.gif]]<br /> <br /> When calculating the center of mass for a continuous distribution of mass, the expression becomes an infinite sum that can be expressed in the form of an integral.<br /> <br /> [[File:Ahuynh4.gif]]<br /> <br /> ----<br /> <br /> ==Examples==<br /> <br /> Be sure to show all steps in your solution and include diagrams whenever possible<br /> <br /> ===Simple===<br /> ===Middling===<br /> ===Difficult===<br /> <br /> ==Connectedness==<br /> #How is this topic connected to something that you are interested in?<br /> #How is it connected to your major?<br /> #Is there an interesting industrial application?<br /> <br /> ==History==<br /> <br /> Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.<br /> <br /> == See also ==<br /> <br /> Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?<br /> <br /> ===Further reading===<br /> <br /> Books, Articles or other print media on this topic<br /> <br /> ===External links===<br /> <br /> Internet resources on this topic<br /> <br /> ==References==<br /> <br /> This section contains the the references you used while writing this page<br /> <br /> [[Category:Which Category did you place this in?]]</div>

Migitalex http://www.physicsbook.gatech.edu/index.php?title=Center_of_Mass&diff=6771 2015-12-01T22:30:15Z

<p>Migitalex: /* The Main Idea */</p> <hr /> <div>Claimed by Alex Huynh (ahuynh9)<br /> <br /> ==The Main Idea==<br /> <br /> The center of mass of an object is the point in space where if a force was applied, the object moves according to Newton's laws without rotation. At the center of mass, the distribution of mass is balanced, and the average of the weighted position coordinates of the distributed mass defines its coordinates. Mechanical calculations are often simplified with respect to the center of mass of objects.<br /> <br /> [[File:Ahuynh5.png]]<br /> ----<br /> <br /> ===A Mathematical Model===<br /> <br /> The position of the center of mass of an object can be found by summating the product of each point mass and its relative linear position and dividing by the sum by the total mass.<br /> <br /> [[File:Ahuynh3.png]]<br /> <br /> This equation can then be extended to three dimensions.<br /> <br /> [[File:Ahuynh1.gif]]<br /> <br /> When calculating the center of mass for a continuous distribution of mass, the expression becomes an infinite sum that can be expressed in the form of an integral.<br /> <br /> [[File:Ahuynh4.gif]]<br /> <br /> This expression can also be used to calculate the center of mass of an object with discontinuous density.<br /> <br /> ----<br /> <br /> ==Examples==<br /> <br /> Be sure to show all steps in your solution and include diagrams whenever possible<br /> <br /> ===Simple===<br /> ===Middling===<br /> ===Difficult===<br /> <br /> ==Connectedness==<br /> #How is this topic connected to something that you are interested in?<br /> #How is it connected to your major?<br /> #Is there an interesting industrial application?<br /> <br /> ==History==<br /> <br /> Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.<br /> <br /> == See also ==<br /> <br /> Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?<br /> <br /> ===Further reading===<br /> <br /> Books, Articles or other print media on this topic<br /> <br /> ===External links===<br /> <br /> Internet resources on this topic<br /> <br /> ==References==<br /> <br /> This section contains the the references you used while writing this page<br /> <br /> [[Category:Which Category did you place this in?]]</div>

Migitalex http://www.physicsbook.gatech.edu/index.php?title=File:Ahuynh5.png&diff=6768 2015-12-01T22:29:49Z

<p>Migitalex: </p> <hr /> <div></div>

Migitalex http://www.physicsbook.gatech.edu/index.php?title=Center_of_Mass&diff=6763 2015-12-01T22:28:20Z

<p>Migitalex: /* A Computational Model */</p> <hr /> <div>Claimed by Alex Huynh (ahuynh9)<br /> <br /> ==The Main Idea==<br /> <br /> The center of mass of an object is the point in space where if a force was applied, the object moves according to Newton's laws without rotation. At the center of mass, the distribution of mass is balanced, and the average of the weighted position coordinates of the distributed mass defines its coordinates. Mechanical calculations are often simplified with respect to the center of mass of objects.<br /> <br /> ----<br /> <br /> ===A Mathematical Model===<br /> <br /> The position of the center of mass of an object can be found by summating the product of each point mass and its relative linear position and dividing by the sum by the total mass.<br /> <br /> [[File:Ahuynh3.png]]<br /> <br /> This equation can then be extended to three dimensions.<br /> <br /> [[File:Ahuynh1.gif]]<br /> <br /> When calculating the center of mass for a continuous distribution of mass, the expression becomes an infinite sum that can be expressed in the form of an integral.<br /> <br /> [[File:Ahuynh4.gif]]<br /> <br /> This expression can also be used to calculate the center of mass of an object with discontinuous density.<br /> <br /> ==Examples==<br /> <br /> Be sure to show all steps in your solution and include diagrams whenever possible<br /> <br /> ===Simple===<br /> ===Middling===<br /> ===Difficult===<br /> <br /> ==Connectedness==<br /> #How is this topic connected to something that you are interested in?<br /> #How is it connected to your major?<br /> #Is there an interesting industrial application?<br /> <br /> ==History==<br /> <br /> Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.<br /> <br /> == See also ==<br /> <br /> Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?<br /> <br /> ===Further reading===<br /> <br /> Books, Articles or other print media on this topic<br /> <br /> ===External links===<br /> <br /> Internet resources on this topic<br /> <br /> ==References==<br /> <br /> This section contains the the references you used while writing this page<br /> <br /> [[Category:Which Category did you place this in?]]</div>

Migitalex http://www.physicsbook.gatech.edu/index.php?title=Center_of_Mass&diff=6760 2015-12-01T22:27:29Z

<p>Migitalex: /* A Mathematical Model */</p> <hr /> <div>Claimed by Alex Huynh (ahuynh9)<br /> <br /> ==The Main Idea==<br /> <br /> The center of mass of an object is the point in space where if a force was applied, the object moves according to Newton's laws without rotation. At the center of mass, the distribution of mass is balanced, and the average of the weighted position coordinates of the distributed mass defines its coordinates. Mechanical calculations are often simplified with respect to the center of mass of objects.<br /> <br /> ----<br /> <br /> ===A Mathematical Model===<br /> <br /> The position of the center of mass of an object can be found by summating the product of each point mass and its relative linear position and dividing by the sum by the total mass.<br /> <br /> [[File:Ahuynh3.png]]<br /> <br /> This equation can then be extended to three dimensions.<br /> <br /> [[File:Ahuynh1.gif]]<br /> <br /> When calculating the center of mass for a continuous distribution of mass, the expression becomes an infinite sum that can be expressed in the form of an integral.<br /> <br /> [[File:Ahuynh4.gif]]<br /> <br /> This expression can also be used to calculate the center of mass of an object with discontinuous density.<br /> <br /> ===A Computational Model===<br /> <br /> How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]<br /> <br /> ==Examples==<br /> <br /> Be sure to show all steps in your solution and include diagrams whenever possible<br /> <br /> ===Simple===<br /> ===Middling===<br /> ===Difficult===<br /> <br /> ==Connectedness==<br /> #How is this topic connected to something that you are interested in?<br /> #How is it connected to your major?<br /> #Is there an interesting industrial application?<br /> <br /> ==History==<br /> <br /> Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.<br /> <br /> == See also ==<br /> <br /> Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?<br /> <br /> ===Further reading===<br /> <br /> Books, Articles or other print media on this topic<br /> <br /> ===External links===<br /> <br /> Internet resources on this topic<br /> <br /> ==References==<br /> <br /> This section contains the the references you used while writing this page<br /> <br /> [[Category:Which Category did you place this in?]]</div>

Migitalex http://www.physicsbook.gatech.edu/index.php?title=Center_of_Mass&diff=6753 2015-12-01T22:24:35Z

<p>Migitalex: /* A Mathematical Model */</p> <hr /> <div>Claimed by Alex Huynh (ahuynh9)<br /> <br /> ==The Main Idea==<br /> <br /> The center of mass of an object is the point in space where if a force was applied, the object moves according to Newton's laws without rotation. At the center of mass, the distribution of mass is balanced, and the average of the weighted position coordinates of the distributed mass defines its coordinates. Mechanical calculations are often simplified with respect to the center of mass of objects.<br /> <br /> ----<br /> <br /> ===A Mathematical Model===<br /> <br /> The position of the center of mass of an object can be found by summating the product of each point mass and its relative linear position and dividing by the sum by the total mass.<br /> <br /> [[File:Ahuynh3.png]]<br /> <br /> This equation can then be extended to three dimensions.<br /> <br /> [[File:Ahuynh1.gif]]<br /> <br /> When calculating the center of mass for a continuous distribution of mass, the expression becomes an infinite sum that can be expressed in the form of an integral.<br /> <br /> [[File:Ahuynh4.gif]]<br /> <br /> ===A Computational Model===<br /> <br /> How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]<br /> <br /> ==Examples==<br /> <br /> Be sure to show all steps in your solution and include diagrams whenever possible<br /> <br /> ===Simple===<br /> ===Middling===<br /> ===Difficult===<br /> <br /> ==Connectedness==<br /> #How is this topic connected to something that you are interested in?<br /> #How is it connected to your major?<br /> #Is there an interesting industrial application?<br /> <br /> ==History==<br /> <br /> Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.<br /> <br /> == See also ==<br /> <br /> Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?<br /> <br /> ===Further reading===<br /> <br /> Books, Articles or other print media on this topic<br /> <br /> ===External links===<br /> <br /> Internet resources on this topic<br /> <br /> ==References==<br /> <br /> This section contains the the references you used while writing this page<br /> <br /> [[Category:Which Category did you place this in?]]</div>

Migitalex http://www.physicsbook.gatech.edu/index.php?title=File:Ahuynh4.gif&diff=6752 2015-12-01T22:24:24Z

<p>Migitalex: </p> <hr /> <div></div>

Migitalex http://www.physicsbook.gatech.edu/index.php?title=Center_of_Mass&diff=6732 2015-12-01T22:17:56Z

<p>Migitalex: /* A Mathematical Model */</p> <hr /> <div>Claimed by Alex Huynh (ahuynh9)<br /> <br /> ==The Main Idea==<br /> <br /> The center of mass of an object is the point in space where if a force was applied, the object moves according to Newton's laws without rotation. At the center of mass, the distribution of mass is balanced, and the average of the weighted position coordinates of the distributed mass defines its coordinates. Mechanical calculations are often simplified with respect to the center of mass of objects.<br /> <br /> ----<br /> <br /> ===A Mathematical Model===<br /> <br /> The position of the center of mass of an object can be found by summating the product of each point mass and its relative linear position and dividing by the sum by the total mass.<br /> <br /> [[File:Ahuynh3.png]]<br /> <br /> This equation can then be extended to three dimensions.<br /> <br /> [[File:Ahuynh1.gif]]<br /> <br /> ===A Computational Model===<br /> <br /> How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]<br /> <br /> ==Examples==<br /> <br /> Be sure to show all steps in your solution and include diagrams whenever possible<br /> <br /> ===Simple===<br /> ===Middling===<br /> ===Difficult===<br /> <br /> ==Connectedness==<br /> #How is this topic connected to something that you are interested in?<br /> #How is it connected to your major?<br /> #Is there an interesting industrial application?<br /> <br /> ==History==<br /> <br /> Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.<br /> <br /> == See also ==<br /> <br /> Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?<br /> <br /> ===Further reading===<br /> <br /> Books, Articles or other print media on this topic<br /> <br /> ===External links===<br /> <br /> Internet resources on this topic<br /> <br /> ==References==<br /> <br /> This section contains the the references you used while writing this page<br /> <br /> [[Category:Which Category did you place this in?]]</div>

Migitalex http://www.physicsbook.gatech.edu/index.php?title=File:Ahuynh3.png&diff=6726 2015-12-01T22:16:48Z

<p>Migitalex: </p> <hr /> <div></div>

Migitalex http://www.physicsbook.gatech.edu/index.php?title=Center_of_Mass&diff=6719 2015-12-01T22:12:10Z

<p>Migitalex: /* The Main Idea */</p> <hr /> <div>Claimed by Alex Huynh (ahuynh9)<br /> <br /> ==The Main Idea==<br /> <br /> The center of mass of an object is the point in space where if a force was applied, the object moves according to Newton's laws without rotation. At the center of mass, the distribution of mass is balanced, and the average of the weighted position coordinates of the distributed mass defines its coordinates. Mechanical calculations are often simplified with respect to the center of mass of objects.<br /> <br /> ----<br /> <br /> ===A Mathematical Model===<br /> <br /> The position of the center of mass of an object can be found by summating the product of each point mass and its relative linear position and dividing by the sum by the total mass.<br /> --[[User:Migitalex|Migitalex]] ([[User talk:Migitalex|talk]]) 17:12, 1 December 2015 (EST)<br /> [[File:Ahuynh2.gif]]<br /> This equation can then be extended to three dimensions.<br /> [[File:Ahuynh1.gif]]<br /> <br /> ===A Computational Model===<br /> <br /> How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]<br /> <br /> ==Examples==<br /> <br /> Be sure to show all steps in your solution and include diagrams whenever possible<br /> <br /> ===Simple===<br /> ===Middling===<br /> ===Difficult===<br /> <br /> ==Connectedness==<br /> #How is this topic connected to something that you are interested in?<br /> #How is it connected to your major?<br /> #Is there an interesting industrial application?<br /> <br /> ==History==<br /> <br /> Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.<br /> <br /> == See also ==<br /> <br /> Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?<br /> <br /> ===Further reading===<br /> <br /> Books, Articles or other print media on this topic<br /> <br /> ===External links===<br /> <br /> Internet resources on this topic<br /> <br /> ==References==<br /> <br /> This section contains the the references you used while writing this page<br /> <br /> [[Category:Which Category did you place this in?]]</div>

Migitalex http://www.physicsbook.gatech.edu/index.php?title=Center_of_Mass&diff=6716 2015-12-01T22:11:36Z

<p>Migitalex: /* A Mathematical Model */</p> <hr /> <div>Claimed by Alex Huynh (ahuynh9)<br /> <br /> ==The Main Idea==<br /> <br /> The center of mass of an object is the point in space where if a force was applied, the object moves according to Newton's laws without rotation. At the center of mass, the distribution of mass is balanced, and the average of the weighted position coordinates of the distributed mass defines its coordinates. Mechanical calculations are often simplified with respect to the center of mass of objects.<br /> <br /> ===A Mathematical Model===<br /> <br /> The position of the center of mass of an object can be found by summating the product of each point mass and its relative linear position and dividing by the sum by the total mass.<br /> <br /> ----<br /> <br /> [[File:Ahuynh2.gif]]<br /> This equation can then be extended to three dimensions.<br /> [[File:Ahuynh1.gif]]<br /> <br /> ===A Computational Model===<br /> <br /> How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]<br /> <br /> ==Examples==<br /> <br /> Be sure to show all steps in your solution and include diagrams whenever possible<br /> <br /> ===Simple===<br /> ===Middling===<br /> ===Difficult===<br /> <br /> ==Connectedness==<br /> #How is this topic connected to something that you are interested in?<br /> #How is it connected to your major?<br /> #Is there an interesting industrial application?<br /> <br /> ==History==<br /> <br /> Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.<br /> <br /> == See also ==<br /> <br /> Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?<br /> <br /> ===Further reading===<br /> <br /> Books, Articles or other print media on this topic<br /> <br /> ===External links===<br /> <br /> Internet resources on this topic<br /> <br /> ==References==<br /> <br /> This section contains the the references you used while writing this page<br /> <br /> [[Category:Which Category did you place this in?]]</div>

Migitalex http://www.physicsbook.gatech.edu/index.php?title=Center_of_Mass&diff=6714 2015-12-01T22:11:00Z

<p>Migitalex: /* A Mathematical Model */</p> <hr /> <div>Claimed by Alex Huynh (ahuynh9)<br /> <br /> ==The Main Idea==<br /> <br /> The center of mass of an object is the point in space where if a force was applied, the object moves according to Newton's laws without rotation. At the center of mass, the distribution of mass is balanced, and the average of the weighted position coordinates of the distributed mass defines its coordinates. Mechanical calculations are often simplified with respect to the center of mass of objects.<br /> <br /> ===A Mathematical Model===<br /> <br /> The position of the center of mass of an object can be found by summating the product of each point mass and its relative linear position and dividing by the sum by the total mass<br /> [[File:Ahuynh2.gif]]<br /> This equation can then be extended to three dimensions.<br /> [[File:Ahuynh1.gif]]<br /> <br /> ===A Computational Model===<br /> <br /> How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]<br /> <br /> ==Examples==<br /> <br /> Be sure to show all steps in your solution and include diagrams whenever possible<br /> <br /> ===Simple===<br /> ===Middling===<br /> ===Difficult===<br /> <br /> ==Connectedness==<br /> #How is this topic connected to something that you are interested in?<br /> #How is it connected to your major?<br /> #Is there an interesting industrial application?<br /> <br /> ==History==<br /> <br /> Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.<br /> <br /> == See also ==<br /> <br /> Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?<br /> <br /> ===Further reading===<br /> <br /> Books, Articles or other print media on this topic<br /> <br /> ===External links===<br /> <br /> Internet resources on this topic<br /> <br /> ==References==<br /> <br /> This section contains the the references you used while writing this page<br /> <br /> [[Category:Which Category did you place this in?]]</div>

Migitalex http://www.physicsbook.gatech.edu/index.php?title=File:Ahuynh2.gif&diff=6710 2015-12-01T22:09:32Z

<p>Migitalex: </p> <hr /> <div></div>

Migitalex