http://www.physicsbook.gatech.edu/api.php?action=feedcontributions&feedformat=atom&user=Akumar 2026-05-01T22:02:15Z User contributions MediaWiki 1.42.7 http://www.physicsbook.gatech.edu/index.php?title=Curving_Motion&diff=13311 2015-12-05T03:51:37Z

<p>Akumar: </p> <hr /> <div>claimed by Aayush Kumar<br /> <br /> Short Description of Topic:<br /> The momentum of an object is nonconstant when it is traveling along a curved path, regardless of whether or not it's speed along the curve is changing.<br /> ==The Main Idea==<br /> <br /> Such cases of curving motion can be analyzed using the properties of the parallel and perpendicular components of net Force as well as understanding the motion's &quot;Kissing Circle&quot;.<br /> <br /> ==Parallel and Perpendicular Components of &lt;math&gt;{\frac{d\vec{p}}{dt}}&lt;/math&gt;==<br /> <br /> ===Perpendicular Component and the Kissing Circle===<br /> This is perhaps the most crucial element of this topic, as a property of smoothly continuous curving motion is that the perpendicular component of the change in momentum is &lt;math&gt;{\frac{d\vec{p}}{dt}}_{perpendicular}=\frac{m v^{2}}{R}&lt;/math&gt; where m is the mass of the object, v is the magnitude of its velocity, and R is the radius of the kissing circle, which we will explain shortly. In essence, the kissing circle of the object is the imaginary circular arc that it temporarily follows along its curved motion, where the radius is the distance to the center of said imaginary circle.<br /> <br /> [[File:Osculating circle.svg|Kissing Circle]]<br /> <br /> In the diagram above, we see that for a curved motion C, the kissing circle when the object is at point P is shown with the blue circle, where the radius is indicated by the red arrow. Often, there are several types of kissing circles within an object's curving motion, so we have to look at the the instantaneous situation to derive instantaneous values. The tangential straight blue line segways into our next topic, the parallel component of the change in momentum.<br /> <br /> ===Parallel Component and Tangential Properties of Curving Motion===<br /> There are two scenarios of curving motion that we will entertain here, one where an object is not changing speed along its curved path and another where the object speeds up or slows down along this curved path. We will start with the constant speed scenario:<br /> <br /> &lt;math&gt;{\frac{d\vec{p}}{dt}}_{parallel}=\vec(0)&lt;/math&gt;<br /> <br /> When an object's tangential velocity is constant throughout the entire motion, we can say that the parallel component of &lt;math&gt;{\frac{d\vec{p}}{dt}}&lt;/math&gt; is zero, as any change in momentum is solely for altering the direction of the object's momentum as opposed to its magnitude. To understand this in more mathematical terms, the only way the magnitude of a momentum vector can be changed is if some component of the force acting on the object lies in the direction of the objects motion. Otherwise, the net force must be in the perpendicular direction towards the center of the kissing circle, like shown below:<br /> <br /> [[File:Vector-diagram.png|Kissing Circle]]<br /> <br /> Here we see that the tangential velocities indicated by the red arrows are all of the same magnitude, and the only thing altering them is the centripetal acceleration, which leads into our discussion of centripetal and centrifugal forces later. Now we will consider cases where &lt;math&gt;{\frac{d\vec{p}}{dt}}&lt;/math&gt; is nonzero. In these cases, the speed of the object along it's curved path is changing and our net force vector has a component that is parallel to the object's tangential motion.<br /> <br /> ===Calculating &lt;math&gt;{\frac{d\vec{p}}{dt}}_{parallel}&lt;/math&gt; and &lt;math&gt;{\frac{d\vec{p}}{dt}}_{perpendicular}&lt;/math&gt;<br /> Given a instantaneous force acting on the object as well as it's initial momentum, we can calculate the final momentum using the Momentum Principle and then observe any change in magnitude between these two vector quantities. Here, &lt;math&gt;{\frac{d\vec{p}}{dt}}_{parallel}&lt;/math&gt; is equal to the difference between the magnitudes of the initial and final momentum divided by the change in time. From this, we can calculate &lt;math&gt;{\frac{d\vec{p}}{dt}}_{perpendicular}&lt;/math&gt; by subtracting &lt;math&gt;{\frac{d\vec{p}}{dt}}_{parallel}&lt;/math&gt; from the net change in momentum. <br /> <br /> ===A Computational Model Example===<br /> Here's a glowscript animation utilizing this method of calculating the parallel and perpendicular components of &lt;math&gt;{\frac{d\vec{p}}{dt}}&lt;/math&gt; is linked below:<br /> <br /> [http://www.glowscript.org/#/user/aayush.kumarmail/folder/Private/program/SpaceVoyageandCurvingMotion Curving Motion with a Satellite Projectile]<br /> <br /> ===Centripetal and Centrifugal Forces===<br /> The Centripetal and Centrifugal Forces of an object in motion demonstrate reciprocity in that the Centripetal Force acts inward towards the center of the kissing circle whereas the centrifugal force is the object's tendency to fly outward.<br /> <br /> ===Simple===<br /> It's fairly simple identifying cases of curving motion, in which case a person can easily apply &lt;math&gt;{\frac{m v^{2}}{R}}&lt;/math&gt; to a situation immediately.<br /> <br /> ===Middling===<br /> Occasionally it can be difficult to gauge any components that influence the object's tangential velocity and effectively speed up or slow down the object by altering the magnitude of the momentum vector.<br /> <br /> ===Difficult===<br /> It can be fairly difficult to understand when there are other factors that influence the perpendicular component of the change of momentum, or when an individual needs to identify another influential force in that axis. For instance, in the Ferris Wheel example, when asked about having to find the necessary velocity for the rider to feel weightless, the individual needs to understand that there's a surface contact force that is also in play and in this case needs to be 0, in which case gravitational force is equal to &lt;math&gt;{\frac{m v^{2}}{R}}&lt;/math&gt;.<br /> <br /> ==Connectedness==<br /> #How is this topic connected to something that you are interested in?<br /> Curving motion is heavily employed when observing planetary orbits, something I find highly fascinating. Although in reality these orbits aren't perfectly circular as we often make them out to be, they still heavily demonstrate the ideas of curving motion and especially &lt;math&gt;{\frac{m v^{2}}{R}}&lt;/math&gt;!<br /> <br /> #How is it connected to your major?<br /> As of now I am a CS major, and using vPython to model curving motion animations among many things helps apply programming ideas such as iteration and variable update.<br /> <br /> #Is there an interesting industrial application?<br /> Centripetal and Centrifugal forces can be found in many industrial applications, as curved motion is a very frequent occurrence when observing interactions between various objects. For instance, a centrifuge using these mechanics helps astronauts train for higher effective gravity.<br /> <br /> [[Category:Momentum]]</div>

Akumar http://www.physicsbook.gatech.edu/index.php?title=Curving_Motion&diff=13235 2015-12-05T03:19:43Z

<p>Akumar: </p> <hr /> <div>claimed by Aayush Kumar<br /> <br /> Short Description of Topic:<br /> The momentum of an object is nonconstant when it is traveling along a curved path, regardless of whether or not it's speed along the curve is changing.<br /> ==The Main Idea==<br /> <br /> Such cases of curving motion can be analyzed using the properties of the parallel and perpendicular components of net Force as well as understanding the motion's &quot;Kissing Circle&quot;.<br /> <br /> ==Parallel and Perpendicular Components of &lt;math&gt;{\frac{d\vec{p}}{dt}}&lt;/math&gt;==<br /> <br /> ===Perpendicular Component and the Kissing Circle===<br /> This is perhaps the most crucial element of this topic, as a property of smoothly continuous curving motion is that the perpendicular component of the change in momentum is &lt;math&gt;{\frac{d\vec{p}}{dt}}_{perpendicular}=\frac{m v^{2}}{R}&lt;/math&gt; where m is the mass of the object, v is the magnitude of its velocity, and R is the radius of the kissing circle, which we will explain shortly. In essence, the kissing circle of the object is the imaginary circular arc that it temporarily follows along its curved motion, where the radius is the distance to the center of said imaginary circle.<br /> <br /> [[File:Osculating circle.svg|Kissing Circle]]<br /> <br /> In the diagram above, we see that for a curved motion C, the kissing circle when the object is at point P is shown with the blue circle, where the radius is indicated by the red arrow. Often, there are several types of kissing circles within an object's curving motion, so we have to look at the the instantaneous situation to derive instantaneous values. The tangential straight blue line segways into our next topic, the parallel component of the change in momentum.<br /> <br /> ===Parallel Component and Tangential Properties of Curving Motion===<br /> There are two scenarios of curving motion that we will entertain here, one where an object is not changing speed along its curved path and another where the object speeds up or slows down along this curved path. We will start with the constant speed scenario:<br /> <br /> &lt;math&gt;{\frac{d\vec{p}}{dt}}_{parallel}=\vec(0)&lt;/math&gt;<br /> <br /> When an object's tangential velocity is constant throughout the entire motion, we can say that the parallel component of &lt;math&gt;{\frac{d\vec{p}}{dt}}&lt;/math&gt; is zero, as any change in momentum is solely for altering the direction of the object's momentum as opposed to its magnitude. To understand this in more mathematical terms, the only way the magnitude of a momentum vector can be changed is if some component of the force acting on the object lies in the direction of the objects motion. Otherwise, the net force must be in the perpendicular direction towards the center of the kissing circle, like shown below:<br /> <br /> [[File:Vector-diagram.png|Kissing Circle]]<br /> <br /> Here we see that the tangential velocities indicated by the red arrows are all of the same magnitude, and the only thing altering them is the centripetal acceleration, which leads into our discussion of centripetal and centrifugal forces later. Now we will consider cases where &lt;math&gt;{\frac{d\vec{p}}{dt}}&lt;/math&gt; is nonzero. In these cases, the speed of the object along it's curved path is changing and our net force vector has a component that is parallel to the object's tangential motion.<br /> <br /> ===Calculating &lt;math&gt;{\frac{d\vec{p}}{dt}}_{parallel}&lt;/math&gt; and &lt;math&gt;{\frac{d\vec{p}}{dt}}_{perpendicular}&lt;/math&gt;<br /> Given a instantaneous force acting on the object as well as it's initial momentum, we can calculate the final momentum using the Momentum Principle and then observe any change in magnitude between these two vector quantities. Here, &lt;math&gt;{\frac{d\vec{p}}{dt}}_{parallel}&lt;/math&gt; is equal to the difference between the magnitudes of the initial and final momentum divided by the change in time. From this, we can calculate &lt;math&gt;{\frac{d\vec{p}}{dt}}_{perpendicular}&lt;/math&gt; by subtracting &lt;math&gt;{\frac{d\vec{p}}{dt}}_{parallel}&lt;/math&gt; from the net change in momentum. <br /> <br /> ===A Computational Model===<br /> Here's a glowscript animation utilizing this method of calculating the parallel and perpendicular components of &lt;math&gt;{\frac{d\vec{p}}{dt}}&lt;/math&gt; is linked below:<br /> <br /> [http://www.glowscript.org/#/user/aayush.kumarmail/folder/Private/program/SpaceVoyageandCurvingMotion Curving Motion with a Satellite Projectile]<br /> <br /> ===Centripetal and Centrifugal Forces===<br /> The Centripetal and Centrifugal Forces of an object in motion demonstrate reciprocity in that the Centripetal Force acts inward towards the center of the kissing circle whereas the centrifugal force is the object's tendency to fly outward.<br /> <br /> ==Examples==<br /> <br /> Be sure to show all steps in your solution and include diagrams whenever possible<br /> <br /> ===Simple===<br /> It's fairly simple identifying cases of curving motion, in which case a person can easily apply &lt;math&gt;{\frac{m v^{2}}{R}}&lt;/math&gt; to a situation immediately.<br /> <br /> ===Middling===<br /> Occasionally it can be difficult to gauge any components that influence the object's tangential velocity and effectively speed up or slow down the object by altering the magnitude of the momentum vector.<br /> <br /> ===Difficult===<br /> It can be fairly difficult to understand when there are other factors that influence the perpendicular component of the change of momentum, or when an individual needs to identify another influential force in that axis. For instance, in the Ferris Wheel example, when asked about having to find the necessary velocity for the rider to feel weightless, the individual needs to understand that there's a surface contact force that is also in play and in this case needs to be 0, in which case gravitational force is equal to &lt;math&gt;{\frac{m v^{2}}{R}}&lt;/math&gt;.<br /> <br /> ==Connectedness==<br /> #How is this topic connected to something that you are interested in?<br /> Curving motion is heavily employed when observing planetary orbits, something I find highly fascinating. Although in reality these orbits aren't perfectly circular as we often make them out to be, they still heavily demonstrate the ideas of curving motion and especially &lt;math&gt;{\frac{m v^{2}}{R}}&lt;/math&gt;!<br /> <br /> #How is it connected to your major?<br /> As of now I am a CS major, and using vPython to model curving motion animations among many things helps apply programming ideas such as iteration and variable update.<br /> <br /> #Is there an interesting industrial application?<br /> Centripetal and Centrifugal forces can be found in many industrial applications, as curved motion is a very frequent occurrence when observing interactions between various objects. For instance, a centrifuge using these mechanics helps astronauts train for higher effective gravity.<br /> <br /> [[Category:Momentum]]</div>

Akumar http://www.physicsbook.gatech.edu/index.php?title=Curving_Motion&diff=13226 2015-12-05T03:17:29Z

<p>Akumar: </p> <hr /> <div>claimed by Aayush Kumar<br /> <br /> Short Description of Topic:<br /> The momentum of an object is nonconstant when it is traveling along a curved path, regardless of whether or not it's speed along the curve is changing.<br /> ==The Main Idea==<br /> <br /> Such cases of curving motion can be analyzed using the properties of the parallel and perpendicular components of net Force as well as understanding the motion's &quot;Kissing Circle&quot;.<br /> <br /> ==Parallel and Perpendicular Components of &lt;math&gt;{\frac{d\vec{p}}{dt}}&lt;/math&gt;==<br /> <br /> ===Perpendicular Component and the Kissing Circle===<br /> This is perhaps the most crucial element of this topic, as a property of smoothly continuous curving motion is that the perpendicular component of the change in momentum is &lt;math&gt;{\frac{d\vec{p}}{dt}}_{perpendicular}=\frac{m v^{2}}{R}&lt;/math&gt; where m is the mass of the object, v is the magnitude of its velocity, and R is the radius of the kissing circle, which we will explain shortly. In essence, the kissing circle of the object is the imaginary circular arc that it temporarily follows along its curved motion, where the radius is the distance to the center of said imaginary circle.<br /> <br /> [[File:Osculating circle.svg|Kissing Circle]]<br /> <br /> In the diagram above, we see that for a curved motion C, the kissing circle when the object is at point P is shown with the blue circle, where the radius is indicated by the red arrow. Often, there are several types of kissing circles within an object's curving motion, so we have to look at the the instantaneous situation to derive instantaneous values. The tangential straight blue line segways into our next topic, the parallel component of the change in momentum.<br /> <br /> ===Parallel Component and Tangential Properties of Curving Motion===<br /> There are two scenarios of curving motion that we will entertain here, one where an object is not changing speed along its curved path and another where the object speeds up or slows down along this curved path. We will start with the constant speed scenario:<br /> <br /> &lt;math&gt;{\frac{d\vec{p}}{dt}}_{parallel}=\vec(0)&lt;/math&gt;<br /> <br /> When an object's tangential velocity is constant throughout the entire motion, we can say that the parallel component of &lt;math&gt;{\frac{d\vec{p}}{dt}}&lt;/math&gt; is zero, as any change in momentum is solely for altering the direction of the object's momentum as opposed to its magnitude. To understand this in more mathematical terms, the only way the magnitude of a momentum vector can be changed is if some component of the force acting on the object lies in the direction of the objects motion. Otherwise, the net force must be in the perpendicular direction towards the center of the kissing circle, like shown below:<br /> <br /> [[File:Vector-diagram.png|Kissing Circle]]<br /> <br /> Here we see that the tangential velocities indicated by the red arrows are all of the same magnitude, and the only thing altering them is the centripetal acceleration, which leads into our discussion of centripetal and centrifugal forces later. Now we will consider cases where &lt;math&gt;{\frac{d\vec{p}}{dt}}&lt;/math&gt; is nonzero. In these cases, the speed of the object along it's curved path is changing and our net force vector has a component that is parallel to the object's tangential motion.<br /> <br /> ===Calculating &lt;math&gt;{\frac{d\vec{p}}{dt}}_{parallel}&lt;/math&gt; and &lt;math&gt;{\frac{d\vec{p}}{dt}}_{perpendicular}&lt;/math&gt;<br /> Given a instantaneous force acting on the object as well as it's initial momentum, we can calculate the final momentum using the Momentum Principle and then observe any change in magnitude between these two vector quantities. Here, &lt;math&gt;{\frac{d\vec{p}}{dt}}_{parallel}&lt;/math&gt; is equal to the difference between the magnitudes of the initial and final momentum divided by the change in time. From this, we can calculate &lt;math&gt;{\frac{d\vec{p}}{dt}}_{perpendicular}&lt;/math&gt; by subtracting &lt;math&gt;{\frac{d\vec{p}}{dt}}_{parallel}&lt;/math&gt; from the net change in momentum. <br /> <br /> ===A Computational Model===<br /> Here's a glowscript animation utilizing this method of calculating the parallel and perpendicular components of &lt;math&gt;{\frac{d\vec{p}}{dt}}&lt;/math&gt; is linked below:<br /> <br /> [http://www.glowscript.org/#/user/aayush.kumarmail/folder/Private/program/SpaceVoyageandCurvingMotion Curving Motion with a Satellite Projectile]<br /> <br /> ===Centripetal and Centrifugal Forces===<br /> The Centripetal and Centrifugal Forces of an object in motion demonstrate reciprocity in that the Centripetal Force acts inward towards the center of the kissing circle whereas the centrifugal force is the object's tendency to fly outward.<br /> <br /> ==Examples==<br /> <br /> Be sure to show all steps in your solution and include diagrams whenever possible<br /> <br /> ===Simple===<br /> It's fairly simple identifying cases of curving motion, in which case a person can easily apply &lt;math&gt;{\frac{m v^{2}}{R}}&lt;/math&gt; to a situation immediately<br /> <br /> ===Middling===<br /> Occasionally it can be difficult to gauge <br /> tangential<br /> <br /> ===Difficult===<br /> It can be fairly difficult to understand when there are other factors that influence the perpendicular component of the change of momentum, or when an individual needs to identify another influential force in that axis. For instance, in the Ferris Wheel example, when asked about having to find the necessary velocity for the rider to feel weightless, the individual needs to understand that there's a surface contact force that is also in play and in this case needs to be 0, in which case gravitational force is equal to &lt;math&gt;{\frac{m v^{2}}{R}}&lt;/math&gt;.<br /> <br /> ==Connectedness==<br /> #How is this topic connected to something that you are interested in?<br /> Curving motion is heavily employed when observing planetary orbits, something I find highly fascinating. Although in reality these orbits aren't perfectly circular as we often make them out to be, they still heavily demonstrate the ideas of curving motion and especially &lt;math&gt;{\frac{m v^{2}}{R}}&lt;/math&gt;!<br /> <br /> ##How is it connected to your major?<br /> As of now I am a CS major, and using vPython to model curving motion animations among many things helps apply programming ideas such as iteration and variable update.<br /> <br /> ###Is there an interesting industrial application?<br /> Centripetal and Centrifugal forces can be found in many industrial applications, as curved motion is a very frequent occurrence when observing interactions between various objects. For instance, a centrifuge using these mechanics helps astronauts train for higher effective gravity.<br /> <br /> [[Category:Momentum]]</div>

Akumar http://www.physicsbook.gatech.edu/index.php?title=Curving_Motion&diff=13223 2015-12-05T03:17:00Z

<p>Akumar: </p> <hr /> <div>claimed by Aayush Kumar<br /> <br /> Short Description of Topic:<br /> The momentum of an object is nonconstant when it is traveling along a curved path, regardless of whether or not it's speed along the curve is changing.<br /> ==The Main Idea==<br /> <br /> Such cases of curving motion can be analyzed using the properties of the parallel and perpendicular components of net Force as well as understanding the motion's &quot;Kissing Circle&quot;.<br /> <br /> ==Parallel and Perpendicular Components of &lt;math&gt;{\frac{d\vec{p}}{dt}}&lt;/math&gt;==<br /> <br /> ===Perpendicular Component and the Kissing Circle===<br /> This is perhaps the most crucial element of this topic, as a property of smoothly continuous curving motion is that the perpendicular component of the change in momentum is &lt;math&gt;{\frac{d\vec{p}}{dt}}_{perpendicular}=\frac{m v^{2}}{R}&lt;/math&gt; where m is the mass of the object, v is the magnitude of its velocity, and R is the radius of the kissing circle, which we will explain shortly. In essence, the kissing circle of the object is the imaginary circular arc that it temporarily follows along its curved motion, where the radius is the distance to the center of said imaginary circle.<br /> <br /> [[File:Osculating circle.svg|Kissing Circle]]<br /> <br /> In the diagram above, we see that for a curved motion C, the kissing circle when the object is at point P is shown with the blue circle, where the radius is indicated by the red arrow. Often, there are several types of kissing circles within an object's curving motion, so we have to look at the the instantaneous situation to derive instantaneous values. The tangential straight blue line segways into our next topic, the parallel component of the change in momentum.<br /> <br /> ===Parallel Component and Tangential Properties of Curving Motion===<br /> There are two scenarios of curving motion that we will entertain here, one where an object is not changing speed along its curved path and another where the object speeds up or slows down along this curved path. We will start with the constant speed scenario:<br /> <br /> &lt;math&gt;{\frac{d\vec{p}}{dt}}_{parallel}=\vec(0)&lt;/math&gt;<br /> <br /> When an object's tangential velocity is constant throughout the entire motion, we can say that the parallel component of &lt;math&gt;{\frac{d\vec{p}}{dt}}&lt;/math&gt; is zero, as any change in momentum is solely for altering the direction of the object's momentum as opposed to its magnitude. To understand this in more mathematical terms, the only way the magnitude of a momentum vector can be changed is if some component of the force acting on the object lies in the direction of the objects motion. Otherwise, the net force must be in the perpendicular direction towards the center of the kissing circle, like shown below:<br /> <br /> [[File:Vector-diagram.png|Kissing Circle]]<br /> <br /> Here we see that the tangential velocities indicated by the red arrows are all of the same magnitude, and the only thing altering them is the centripetal acceleration, which leads into our discussion of centripetal and centrifugal forces later. Now we will consider cases where &lt;math&gt;{\frac{d\vec{p}}{dt}}&lt;/math&gt; is nonzero. In these cases, the speed of the object along it's curved path is changing and our net force vector has a component that is parallel to the object's tangential motion.<br /> <br /> ===Calculating &lt;math&gt;{\frac{d\vec{p}}{dt}}_{parallel}&lt;/math&gt; and &lt;math&gt;{\frac{d\vec{p}}{dt}}_{perpendicular}&lt;/math&gt;<br /> Given a instantaneous force acting on the object as well as it's initial momentum, we can calculate the final momentum using the Momentum Principle and then observe any change in magnitude between these two vector quantities. Here, &lt;math&gt;{\frac{d\vec{p}}{dt}}_{parallel}&lt;/math&gt; is equal to the difference between the magnitudes of the initial and final momentum divided by the change in time. From this, we can calculate &lt;math&gt;{\frac{d\vec{p}}{dt}}_{perpendicular}&lt;/math&gt; by subtracting &lt;math&gt;{\frac{d\vec{p}}{dt}}_{parallel}&lt;/math&gt; from the net change in momentum. <br /> <br /> ===A Computational Model===<br /> Here's a glowscript animation utilizing this method of calculating the parallel and perpendicular components of &lt;math&gt;{\frac{d\vec{p}}{dt}}&lt;/math&gt; is linked below:<br /> <br /> [http://www.glowscript.org/#/user/aayush.kumarmail/folder/Private/program/SpaceVoyageandCurvingMotion Curving Motion with a Satellite Projectile]<br /> <br /> ===Centripetal and Centrifugal Forces===<br /> The Centripetal and Centrifugal Forces of an object in motion demonstrate reciprocity in that the Centripetal Force acts inward towards the center of the kissing circle whereas the centrifugal force is the object's tendency to fly outward.<br /> <br /> ==Examples==<br /> <br /> Be sure to show all steps in your solution and include diagrams whenever possible<br /> <br /> ===Simple===<br /> It's fairly simple identifying cases of curving motion, in which case a person can easily apply &lt;math&gt;{\frac{m v^{2}}{R}}&lt;/math&gt; to a situation immediately<br /> <br /> ===Middling===<br /> Occasionally it can be difficult to gauge <br /> tangential<br /> <br /> ===Difficult===<br /> It can be fairly difficult to understand when there are other factors that influence the perpendicular component of the change of momentum, or when an individual needs to identify another influential force in that axis. For instance, in the Ferris Wheel example, when asked about having to find the necessary velocity for the rider to feel weightless, the individual needs to understand that there's a surface contact force that is also in play and in this case needs to be 0, in which case gravitational force is equal to &lt;math&gt;{\frac{m v^{2}}{R}}&lt;/math&gt;.<br /> <br /> ==Connectedness==<br /> #1 How is this topic connected to something that you are interested in?<br /> Curving motion is heavily employed when observing planetary orbits, something I find highly fascinating. Although in reality these orbits aren't perfectly circular as we often make them out to be, they still heavily demonstrate the ideas of curving motion and especially &lt;math&gt;{\frac{m v^{2}}{R}}&lt;/math&gt;!<br /> <br /> #2 How is it connected to your major?<br /> As of now I am a CS major, and using vPython to model curving motion animations among many things helps apply programming ideas such as iteration and variable update.<br /> <br /> #3 Is there an interesting industrial application?<br /> Centripetal and Centrifugal forces can be found in many industrial applications, as curved motion is a very frequent occurrence when observing interactions between various objects. For instance, a centrifuge using these mechanics helps astronauts train for higher effective gravity.<br /> <br /> [[Category:Momentum]]</div>

Akumar http://www.physicsbook.gatech.edu/index.php?title=Curving_Motion&diff=13221 2015-12-05T03:16:21Z

<p>Akumar: </p> <hr /> <div>claimed by Aayush Kumar<br /> <br /> Short Description of Topic:<br /> The momentum of an object is nonconstant when it is traveling along a curved path, regardless of whether or not it's speed along the curve is changing.<br /> ==The Main Idea==<br /> <br /> Such cases of curving motion can be analyzed using the properties of the parallel and perpendicular components of net Force as well as understanding the motion's &quot;Kissing Circle&quot;.<br /> <br /> ==Parallel and Perpendicular Components of &lt;math&gt;{\frac{d\vec{p}}{dt}}&lt;/math&gt;==<br /> <br /> ===Perpendicular Component and the Kissing Circle===<br /> This is perhaps the most crucial element of this topic, as a property of smoothly continuous curving motion is that the perpendicular component of the change in momentum is &lt;math&gt;{\frac{d\vec{p}}{dt}}_{perpendicular}=\frac{m v^{2}}{R}&lt;/math&gt; where m is the mass of the object, v is the magnitude of its velocity, and R is the radius of the kissing circle, which we will explain shortly. In essence, the kissing circle of the object is the imaginary circular arc that it temporarily follows along its curved motion, where the radius is the distance to the center of said imaginary circle.<br /> <br /> [[File:Osculating circle.svg|Kissing Circle]]<br /> <br /> In the diagram above, we see that for a curved motion C, the kissing circle when the object is at point P is shown with the blue circle, where the radius is indicated by the red arrow. Often, there are several types of kissing circles within an object's curving motion, so we have to look at the the instantaneous situation to derive instantaneous values. The tangential straight blue line segways into our next topic, the parallel component of the change in momentum.<br /> <br /> ===Parallel Component and Tangential Properties of Curving Motion===<br /> There are two scenarios of curving motion that we will entertain here, one where an object is not changing speed along its curved path and another where the object speeds up or slows down along this curved path. We will start with the constant speed scenario:<br /> <br /> &lt;math&gt;{\frac{d\vec{p}}{dt}}_{parallel}=\vec(0)&lt;/math&gt;<br /> <br /> When an object's tangential velocity is constant throughout the entire motion, we can say that the parallel component of &lt;math&gt;{\frac{d\vec{p}}{dt}}&lt;/math&gt; is zero, as any change in momentum is solely for altering the direction of the object's momentum as opposed to its magnitude. To understand this in more mathematical terms, the only way the magnitude of a momentum vector can be changed is if some component of the force acting on the object lies in the direction of the objects motion. Otherwise, the net force must be in the perpendicular direction towards the center of the kissing circle, like shown below:<br /> <br /> [[File:Vector-diagram.png|Kissing Circle]]<br /> <br /> Here we see that the tangential velocities indicated by the red arrows are all of the same magnitude, and the only thing altering them is the centripetal acceleration, which leads into our discussion of centripetal and centrifugal forces later. Now we will consider cases where &lt;math&gt;{\frac{d\vec{p}}{dt}}&lt;/math&gt; is nonzero. In these cases, the speed of the object along it's curved path is changing and our net force vector has a component that is parallel to the object's tangential motion.<br /> <br /> ===Calculating &lt;math&gt;{\frac{d\vec{p}}{dt}}_{parallel}&lt;/math&gt; and &lt;math&gt;{\frac{d\vec{p}}{dt}}_{perpendicular}&lt;/math&gt;<br /> Given a instantaneous force acting on the object as well as it's initial momentum, we can calculate the final momentum using the Momentum Principle and then observe any change in magnitude between these two vector quantities. Here, &lt;math&gt;{\frac{d\vec{p}}{dt}}_{parallel}&lt;/math&gt; is equal to the difference between the magnitudes of the initial and final momentum divided by the change in time. From this, we can calculate &lt;math&gt;{\frac{d\vec{p}}{dt}}_{perpendicular}&lt;/math&gt; by subtracting &lt;math&gt;{\frac{d\vec{p}}{dt}}_{parallel}&lt;/math&gt; from the net change in momentum. <br /> <br /> ===A Computational Model===<br /> Here's a glowscript animation utilizing this method of calculating the parallel and perpendicular components of &lt;math&gt;{\frac{d\vec{p}}{dt}}&lt;/math&gt; is linked below:<br /> <br /> [http://www.glowscript.org/#/user/aayush.kumarmail/folder/Private/program/SpaceVoyageandCurvingMotion Curving Motion with a Satellite Projectile]<br /> <br /> ===Centripetal and Centrifugal Forces===<br /> The Centripetal and Centrifugal Forces of an object in motion demonstrate reciprocity in that the Centripetal Force acts inward towards the center of the kissing circle whereas the centrifugal force is the object's tendency to fly outward.<br /> <br /> ==Examples==<br /> <br /> Be sure to show all steps in your solution and include diagrams whenever possible<br /> <br /> ===Simple===<br /> It's fairly simple identifying cases of curving motion, in which case a person can easily apply &lt;math&gt;{\frac{m v^{2}}{R}}&lt;/math&gt; to a situation immediately<br /> <br /> ===Middling===<br /> Occasionally it can be difficult to gauge <br /> tangential<br /> <br /> ===Difficult===<br /> It can be fairly difficult to understand when there are other factors that influence the perpendicular component of the change of momentum, or when an individual needs to identify another influential force in that axis. For instance, in the Ferris Wheel example, when asked about having to find the necessary velocity for the rider to feel weightless, the individual needs to understand that there's a surface contact force that is also in play and in this case needs to be 0, in which case gravitational force is equal to &lt;math&gt;{\frac{m v^{2}}{R}}&lt;/math&gt;.<br /> <br /> ==Connectedness==<br /> #How is this topic connected to something that you are interested in?<br /> Curving motion is heavily employed when observing planetary orbits, something I find highly fascinating. Although in reality these orbits aren't perfectly circular as we often make them out to be, they still heavily demonstrate the ideas of curving motion and especially &lt;math&gt;{\frac{m v^{2}}{R}}&lt;/math&gt;!<br /> <br /> #How is it connected to your major?<br /> As of now I am a CS major, and using vPython to model curving motion animations among many things helps apply programming ideas such as iteration and variable update.<br /> <br /> #Is there an interesting industrial application?<br /> Centripetal and Centrifugal forces can be found in many industrial applications, as curved motion is a very frequent occurrence when observing interactions between various objects. For instance, a centrifuge using these mechanics helps astronauts train for higher effective gravity.<br /> <br /> [[Category:Momentum]]</div>

Akumar http://www.physicsbook.gatech.edu/index.php?title=Curving_Motion&diff=13212 2015-12-05T03:13:23Z

<p>Akumar: </p> <hr /> <div>claimed by Aayush Kumar<br /> <br /> Short Description of Topic:<br /> The momentum of an object is nonconstant when it is traveling along a curved path, regardless of whether or not it's speed along the curve is changing.<br /> ==The Main Idea==<br /> <br /> Such cases of curving motion can be analyzed using the properties of the parallel and perpendicular components of net Force as well as understanding the motion's &quot;Kissing Circle&quot;.<br /> <br /> ==Parallel and Perpendicular Components of &lt;math&gt;{\frac{d\vec{p}}{dt}}&lt;/math&gt;==<br /> <br /> ===Perpendicular Component and the Kissing Circle===<br /> This is perhaps the most crucial element of this topic, as a property of smoothly continuous curving motion is that the perpendicular component of the change in momentum is &lt;math&gt;{\frac{d\vec{p}}{dt}}_{perpendicular}=\frac{m v^{2}}{R}&lt;/math&gt; where m is the mass of the object, v is the magnitude of its velocity, and R is the radius of the kissing circle, which we will explain shortly. In essence, the kissing circle of the object is the imaginary circular arc that it temporarily follows along its curved motion, where the radius is the distance to the center of said imaginary circle.<br /> <br /> [[File:Osculating circle.svg|Kissing Circle]]<br /> <br /> In the diagram above, we see that for a curved motion C, the kissing circle when the object is at point P is shown with the blue circle, where the radius is indicated by the red arrow. Often, there are several types of kissing circles within an object's curving motion, so we have to look at the the instantaneous situation to derive instantaneous values. The tangential straight blue line segways into our next topic, the parallel component of the change in momentum.<br /> <br /> ===Parallel Component and Tangential Properties of Curving Motion===<br /> There are two scenarios of curving motion that we will entertain here, one where an object is not changing speed along its curved path and another where the object speeds up or slows down along this curved path. We will start with the constant speed scenario:<br /> <br /> &lt;math&gt;{\frac{d\vec{p}}{dt}}_{parallel}=\vec(0)&lt;/math&gt;<br /> <br /> When an object's tangential velocity is constant throughout the entire motion, we can say that the parallel component of &lt;math&gt;{\frac{d\vec{p}}{dt}}&lt;/math&gt; is zero, as any change in momentum is solely for altering the direction of the object's momentum as opposed to its magnitude. To understand this in more mathematical terms, the only way the magnitude of a momentum vector can be changed is if some component of the force acting on the object lies in the direction of the objects motion. Otherwise, the net force must be in the perpendicular direction towards the center of the kissing circle, like shown below:<br /> <br /> [[File:Vector-diagram.png|Kissing Circle]]<br /> <br /> Here we see that the tangential velocities indicated by the red arrows are all of the same magnitude, and the only thing altering them is the centripetal acceleration, which leads into our discussion of centripetal and centrifugal forces later. Now we will consider cases where &lt;math&gt;{\frac{d\vec{p}}{dt}}&lt;/math&gt; is nonzero. In these cases, the speed of the object along it's curved path is changing and our net force vector has a component that is parallel to the object's tangential motion.<br /> <br /> ===Calculating &lt;math&gt;{\frac{d\vec{p}}{dt}}_{parallel}&lt;/math&gt; and &lt;math&gt;{\frac{d\vec{p}}{dt}}_{perpendicular}&lt;/math&gt;<br /> Given a instantaneous force acting on the object as well as it's initial momentum, we can calculate the final momentum using the Momentum Principle and then observe any change in magnitude between these two vector quantities. Here, &lt;math&gt;{\frac{d\vec{p}}{dt}}_{parallel}&lt;/math&gt; is equal to the difference between the magnitudes of the initial and final momentum divided by the change in time. From this, we can calculate &lt;math&gt;{\frac{d\vec{p}}{dt}}_{perpendicular}&lt;/math&gt; by subtracting &lt;math&gt;{\frac{d\vec{p}}{dt}}_{parallel}&lt;/math&gt; from the net change in momentum. <br /> <br /> ===A Computational Model===<br /> Here's a glowscript animation utilizing this method of calculating the parallel and perpendicular components of &lt;math&gt;{\frac{d\vec{p}}{dt}}&lt;/math&gt; is linked below:<br /> <br /> [http://www.glowscript.org/#/user/aayush.kumarmail/folder/Private/program/SpaceVoyageandCurvingMotion Curving Motion with a Satellite Projectile]<br /> <br /> ===Centripetal and Centrifugal Forces===<br /> The Centripetal and Centrifugal Forces of an object in motion demonstrate reciprocity in that the Centripetal Force acts inward towards the center of the kissing circle whereas the centrifugal force is the object's tendency to fly outward.<br /> <br /> ==Examples==<br /> <br /> Be sure to show all steps in your solution and include diagrams whenever possible<br /> <br /> ===Simple===<br /> It's fairly simple identifying cases of curving motion, in which case a person can easily apply &lt;math&gt;{\frac{m v^{2}}{R}}&lt;/math&gt; to a situation immediately<br /> <br /> ===Middling===<br /> Occasionally it can be difficult to gauge <br /> tangential<br /> <br /> ===Difficult===<br /> It can be fairly difficult to understand when <br /> circus wheel dp/dt<br /> <br /> ==Connectedness==<br /> #How is this topic connected to something that you are interested in?<br /> Curving motion is heavily employed when observing planetary orbits, something I find highly fascinating. Although in reality these orbits aren't perfectly circular as we often make them out to be, they still heavily demonstrate the ideas of curving motion and especially &lt;math&gt;{\frac{m v^{2}}{R}}&lt;/math&gt;!<br /> <br /> #How is it connected to your major?<br /> As of now I am a CS major, and using vPython to model curving motion animations among many things helps apply programming ideas such as iteration and variable update.<br /> <br /> #Is there an interesting industrial application?<br /> Centripetal and Centrifugal forces can be found in many industrial applications, as curved motion is a very frequent occurrence when observing interactions between various objects. For instance, a centrifuge using these mechanics helps astronauts train for higher effective gravity.<br /> <br /> [[Category:Momentum]]</div>

Akumar http://www.physicsbook.gatech.edu/index.php?title=Curving_Motion&diff=13171 2015-12-05T02:59:34Z

<p>Akumar: </p> <hr /> <div>claimed by Aayush Kumar<br /> <br /> Short Description of Topic:<br /> The momentum of an object is nonconstant when it is traveling along a curved path, regardless of whether or not it's speed along the curve is changing.<br /> ==The Main Idea==<br /> <br /> Such cases of curving motion can be analyzed using the properties of the parallel and perpendicular components of net Force as well as understanding the motion's &quot;Kissing Circle&quot;.<br /> <br /> ==Parallel and Perpendicular Components of &lt;math&gt;{\frac{d\vec{p}}{dt}}&lt;/math&gt;==<br /> <br /> ===Perpendicular Component and the Kissing Circle===<br /> This is perhaps the most crucial element of this topic, as a property of smoothly continuous curving motion is that the perpendicular component of the change in momentum is &lt;math&gt;{\frac{d\vec{p}}{dt}}_{perpendicular}=\frac{m v^{2}}{R}&lt;/math&gt; where m is the mass of the object, v is the magnitude of its velocity, and R is the radius of the kissing circle, which we will explain shortly. In essence, the kissing circle of the object is the imaginary circular arc that it temporarily follows along its curved motion, where the radius is the distance to the center of said imaginary circle.<br /> <br /> [[File:Osculating circle.svg|Kissing Circle]]<br /> <br /> In the diagram above, we see that for a curved motion C, the kissing circle when the object is at point P is shown with the blue circle, where the radius is indicated by the red arrow. Often, there are several types of kissing circles within an object's curving motion, so we have to look at the the instantaneous situation to derive instantaneous values. The tangential straight blue line segways into our next topic, the parallel component of the change in momentum.<br /> <br /> ===Parallel Component and Tangential Properties of Curving Motion===<br /> There are two scenarios of curving motion that we will entertain here, one where an object is not changing speed along its curved path and another where the object speeds up or slows down along this curved path. We will start with the constant speed scenario:<br /> <br /> &lt;math&gt;{\frac{d\vec{p}}{dt}}_{parallel}=\vec(0)&lt;/math&gt;<br /> <br /> When an object's tangential velocity is constant throughout the entire motion, we can say that the parallel component of &lt;math&gt;{\frac{d\vec{p}}{dt}}&lt;/math&gt; is zero, as any change in momentum is solely for altering the direction of the object's momentum as opposed to its magnitude. To understand this in more mathematical terms, the only way the magnitude of a momentum vector can be changed is if some component of the force acting on the object lies in the direction of the objects motion. Otherwise, the net force must be in the perpendicular direction towards the center of the kissing circle, like shown below:<br /> <br /> [[File:Vector-diagram.png|Kissing Circle]]<br /> <br /> Here we see that the tangential velocities indicated by the red arrows are all of the same magnitude, and the only thing altering them is the centripetal acceleration, which leads into our discussion of centripetal and centrifugal forces later. Now we will consider cases where &lt;math&gt;{\frac{d\vec{p}}{dt}}&lt;/math&gt; is nonzero. In these cases, the speed of the object along it's curved path is changing and our net force vector has a component that is parallel to the object's tangential motion.<br /> <br /> ===Calculating &lt;math&gt;{\frac{d\vec{p}}{dt}}_{parallel}&lt;/math&gt; and &lt;math&gt;{\frac{d\vec{p}}{dt}}_{perpendicular}&lt;/math&gt;<br /> Given a instantaneous force acting on the object as well as it's initial momentum, we can calculate the final momentum using the Momentum Principle and then observe any change in magnitude between these two vector quantities. Here, &lt;math&gt;{\frac{d\vec{p}}{dt}}_{parallel}&lt;/math&gt; is equal to the difference between the magnitudes of the initial and final momentum divided by the change in time. From this, we can calculate &lt;math&gt;{\frac{d\vec{p}}{dt}}_{perpendicular}&lt;/math&gt; by subtracting &lt;math&gt;{\frac{d\vec{p}}{dt}}_{parallel}&lt;/math&gt; from the net change in momentum. <br /> <br /> ===A Computational Model===<br /> Here's a glowscript animation utilizing this method of calculating the parallel and perpendicular components of &lt;math&gt;{\frac{d\vec{p}}{dt}}&lt;/math&gt; is linked below:<br /> <br /> [http://www.glowscript.org/#/user/aayush.kumarmail/folder/Private/program/SpaceVoyageandCurvingMotion Curving Motion with a Satellite Projectile]<br /> <br /> ===Centripetal and Centrifugal Forces===<br /> The Centripetal and Centrifugal Forces of an object in motion demonstrate reciprocity in that the Centripetal Force acts inward towards the center of the kissing circle whereas the centrifugal force is the object's tendency to fly outward.<br /> <br /> ==Examples==<br /> <br /> Be sure to show all steps in your solution and include diagrams whenever possible<br /> <br /> ===Simple===<br /> It's fairly simple identifying cases of curving motion, in which case a person can easily apply &lt;math&gt;{\frac{m v^{2}}{R}}&lt;/math&gt;<br /> ===Middling===<br /> <br /> ===Difficult===<br /> It can be fairly difficult to understand when <br /> <br /> ==Connectedness==<br /> #How is this topic connected to something that you are interested in?<br /> Curving motion is heavily employed when observing planetary orbits, something I find highly fascinating. Although in reality these orbits aren't perfectly circular as we often<br /> <br /> #How is it connected to your major?<br /> As of now I am a CS major, and using vPython to model curving motion animations among many things helps apply programming ideas such as iteration and variable update.<br /> <br /> #Is there an interesting industrial application?<br /> Centripetal and Centrifugal forces can be found in many industrial applications, as curved motion is a very frequent occurrence when observing interactions between various objects. For instance, a centrifuge using these mechanics helps astronauts train for higher effective gravity.<br /> <br /> [[Category:Momentum]]</div>

Akumar http://www.physicsbook.gatech.edu/index.php?title=Curving_Motion&diff=13086 2015-12-05T02:14:59Z

<p>Akumar: </p> <hr /> <div>claimed by Aayush Kumar<br /> <br /> Short Description of Topic:<br /> The momentum of an object is nonconstant when it is traveling along a curved path, regardless of whether or not it's speed along the curve is changing.<br /> ==The Main Idea==<br /> <br /> Such cases of curving motion can be analyzed using the properties of the parallel and perpendicular components of net Force as well as understanding the motion's &quot;Kissing Circle&quot;.<br /> <br /> ==Parallel and Perpendicular Components of &lt;math&gt;{\frac{d\vec{p}}{dt}}&lt;/math&gt;==<br /> <br /> ===Perpendicular Component and the Kissing Circle===<br /> This is perhaps the most crucial element of this topic, as a property of smoothly continuous curving motion is that the perpendicular component of the change in momentum is &lt;math&gt;{\frac{d\vec{p}}{dt}}_{perpendicular}=\frac{m v^{2}}{R}&lt;/math&gt; where m is the mass of the object, v is the magnitude of its velocity, and R is the radius of the kissing circle, which we will explain shortly. In essence, the kissing circle of the object is the imaginary circular arc that it temporarily follows along its curved motion, where the radius is the distance to the center of said imaginary circle.<br /> <br /> [[File:Osculating circle.svg|Kissing Circle]]<br /> <br /> In the diagram above, we see that for a curved motion C, the kissing circle when the object is at point P is shown with the blue circle, where the radius is indicated by the red arrow. Often, there are several types of kissing circles within an object's curving motion, so we have to look at the the instantaneous situation to derive instantaneous values. The tangential straight blue line segways into our next topic, the parallel component of the change in momentum.<br /> <br /> ===Parallel Component and Tangential Properties of Curving Motion===<br /> There are two scenarios of curving motion that we will entertain here, one where an object is not changing speed along its curved path and another where the object speeds up or slows down along this curved path. We will start with the constant speed scenario:<br /> <br /> &lt;math&gt;{\frac{d\vec{p}}{dt}}_{parallel}=\vec(0)&lt;/math&gt;<br /> <br /> When an object's tangential velocity is constant throughout the entire motion, we can say that the parallel component of &lt;math&gt;{\frac{d\vec{p}}{dt}}&lt;/math&gt; is zero, as any change in momentum is solely for altering the direction of the object's momentum as opposed to its magnitude. To understand this in more mathematical terms, the only way the magnitude of a momentum vector can be changed is if some component of the force acting on the object lies in the direction of the objects motion. Otherwise, the net force must be in the perpendicular direction towards the center of the kissing circle, like shown below:<br /> <br /> [[File:Vector-diagram.png|Kissing Circle]]<br /> <br /> Here we see that the tangential velocities indicated by the red arrows are all of the same magnitude, and the only thing altering them is the centripetal acceleration, which leads into our discussion of centripetal and centrifugal forces later. Now we will consider cases where &lt;math&gt;{\frac{d\vec{p}}{dt}}&lt;/math&gt; is nonzero. In these cases, the speed of the object along it's curved path is changing and our net force vector has a component that is parallel to the object's tangential motion.<br /> <br /> ===Calculating &lt;math&gt;{\frac{d\vec{p}}{dt}}_{parallel}&lt;/math&gt; and &lt;math&gt;{\frac{d\vec{p}}{dt}}_{perpendicular}&lt;/math&gt;<br /> Given a instantaneous force acting on the object as well as it's initial momentum, we can calculate the final momentum using the Momentum Principle and then observe any change in magnitude between these two vector quantities. Here, &lt;math&gt;{\frac{d\vec{p}}{dt}}_{parallel}&lt;/math&gt; is equal to the difference between the magnitudes of the initial and final momentum divided by the change in time. From this, we can calculate &lt;math&gt;{\frac{d\vec{p}}{dt}}_{perpendicular}&lt;/math&gt; by subtracting &lt;math&gt;{\frac{d\vec{p}}{dt}}_{parallel}&lt;/math&gt; from the net change in momentum. <br /> <br /> ===A Computational Model===<br /> Here's a glowscript animation utilizing this method of calculating the parallel and perpendicular components of &lt;math&gt;{\frac{d\vec{p}}{dt}}&lt;/math&gt; is linked below:<br /> <br /> [http://www.glowscript.org/#/user/aayush.kumarmail/folder/Private/program/SpaceVoyageandCurvingMotion Curving Motion with a Satellite Projectile]<br /> <br /> ===Centripetal and Centrifugal Forces===<br /> The Centripetal and Centrifugal Forces of an object in motion demonstrate reciprocity in that the Centripetal Force acts inward towards the center of the kissing circle whereas the centrifugal force is the object's tendency to fly outward.<br /> <br /> ==Examples==<br /> <br /> Be sure to show all steps in your solution and include diagrams whenever possible<br /> <br /> ===Simple===<br /> It's fairly simple identifying cases of curving motion, in which case a person can easily apply &lt;math&gt;{\frac{m v^{2}}{R}}&lt;/math&gt;<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 /> <br /> [[Category:Momentum]]</div>

Akumar http://www.physicsbook.gatech.edu/index.php?title=Curving_Motion&diff=13075 2015-12-05T02:09:10Z

<p>Akumar: </p> <hr /> <div>claimed by Aayush Kumar<br /> <br /> Short Description of Topic:<br /> The momentum of an object is nonconstant when it is traveling along a curved path, regardless of whether or not it's speed along the curve is changing.<br /> ==The Main Idea==<br /> <br /> Such cases of curving motion can be analyzed using the properties of the parallel and perpendicular components of net Force as well as understanding the motion's &quot;Kissing Circle&quot;.<br /> <br /> ==Parallel and Perpendicular Components of &lt;math&gt;{\frac{d\vec{p}}{dt}}&lt;/math&gt;==<br /> <br /> ===Perpendicular Component and the Kissing Circle===<br /> This is perhaps the most crucial element of this topic, as a property of smoothly continuous curving motion is that the perpendicular component of the change in momentum is &lt;math&gt;{\frac{d\vec{p}}{dt}}_{perpendicular}=\frac{m v^{2}}{R}&lt;/math&gt; where m is the mass of the object, v is the magnitude of its velocity, and R is the radius of the kissing circle, which we will explain shortly. In essence, the kissing circle of the object is the imaginary circular arc that it temporarily follows along its curved motion, where the radius is the distance to the center of said imaginary circle.<br /> <br /> [[File:Osculating circle.svg|Kissing Circle]]<br /> <br /> In the diagram above, we see that for a curved motion C, the kissing circle when the object is at point P is shown with the blue circle, where the radius is indicated by the red arrow. Often, there are several types of kissing circles within an object's curving motion, so we have to look at the the instantaneous situation to derive instantaneous values. The tangential straight blue line segways into our next topic, the parallel component of the change in momentum.<br /> <br /> ===Parallel Component and Tangential Properties of Curving Motion===<br /> There are two scenarios of curving motion that we will entertain here, one where an object is not changing speed along its curved path and another where the object speeds up or slows down along this curved path. We will start with the constant speed scenario:<br /> <br /> &lt;math&gt;{\frac{d\vec{p}}{dt}}_{parallel}=\vec(0)&lt;/math&gt;<br /> <br /> When an object's tangential velocity is constant throughout the entire motion, we can say that the parallel component of &lt;math&gt;{\frac{d\vec{p}}{dt}}&lt;/math&gt; is zero, as any change in momentum is solely for altering the direction of the object's momentum as opposed to its magnitude. To understand this in more mathematical terms, the only way the magnitude of a momentum vector can be changed is if some component of the force acting on the object lies in the direction of the objects motion. Otherwise, the net force must be in the perpendicular direction towards the center of the kissing circle, like shown below:<br /> <br /> [[File:Vector-diagram.png|Kissing Circle]]<br /> <br /> Here we see that the tangential velocities indicated by the red arrows are all of the same magnitude, and the only thing altering them is the centripetal acceleration, which leads into our discussion of centripetal and centrifugal forces later. Now we will consider cases where &lt;math&gt;{\frac{d\vec{p}}{dt}}&lt;/math&gt; is nonzero. In these cases, the speed of the object along it's curved path is changing and our net force vector has a component that is parallel to the object's tangential motion.<br /> <br /> ===Calculating &lt;math&gt;{\frac{d\vec{p}}{dt}}_{parallel}&lt;/math&gt; and &lt;math&gt;{\frac{d\vec{p}}{dt}}_{perpendicular}&lt;/math&gt;<br /> Given a instantaneous force acting on the object as well as it's initial momentum, we can calculate the final momentum using the Momentum Principle and then observe any change in magnitude between these two vector quantities. Here, &lt;math&gt;{\frac{d\vec{p}}{dt}}_{parallel}&lt;/math&gt; is equal to the difference between the magnitudes of the initial and final momentum divided by the change in time. From this, we can calculate &lt;math&gt;{\frac{d\vec{p}}{dt}}_{perpendicular}&lt;/math&gt; by subtracting &lt;math&gt;{\frac{d\vec{p}}{dt}}_{parallel}&lt;/math&gt; from the net change in momentum. <br /> <br /> ===A Computational Model===<br /> Here's a glowscript animation utilizing this method of calculating the parallel and perpendicular components of &lt;math&gt;{\frac{d\vec{p}}{dt}}&lt;/math&gt; is linked below:<br /> <br /> [http://www.glowscript.org/#/user/aayush.kumarmail/folder/Private/program/SpaceVoyageandCurvingMotion Curving Motion with a Satellite Projectile]<br /> <br /> ===Centripetal and Centrifugal Forces===<br /> The Centripetal and Centrifugal Forces of an object in motion demonstrate reciprocity in that the Centripetal Force acts inward towards the center of the kissing circle whereas the centrifugal force is the object's tendency to fly outward.<br /> <br /> <br /> [[Category:Momentum]]</div>

Akumar http://www.physicsbook.gatech.edu/index.php?title=Curving_Motion&diff=13006 2015-12-05T01:10:13Z

<p>Akumar: </p> <hr /> <div>claimed by Aayush Kumar<br /> <br /> Short Description of Topic:<br /> The momentum of an object is nonconstant when it is traveling along a curved path, regardless of whether or not it's speed along the curve is changing.<br /> ==The Main Idea==<br /> <br /> Such cases of curving motion can be analyzed using the properties of the parallel and perpendicular components of net Force as well as understanding the motion's &quot;Kissing Circle&quot;.<br /> <br /> ==Parallel and Perpendicular Components of &lt;math&gt;{\frac{d\vec{p}}{dt}}&lt;/math&gt;==<br /> <br /> ===Perpendicular Component and the Kissing Circle===<br /> This is perhaps the most crucial element of this topic, as a property of smoothly continuous curving motion is that the perpendicular component of the change in momentum is &lt;math&gt;{\frac{d\vec{p}}{dt}}_{perpendicular}=\frac{m v^{2}}{R}&lt;/math&gt; where m is the mass of the object, v is the magnitude of its velocity, and R is the radius of the kissing circle, which we will explain shortly. In essence, the kissing circle of the object is the imaginary circular arc that it temporarily follows along its curved motion, where the radius is the distance to the center of said imaginary circle.<br /> <br /> [[File:Osculating circle.svg|Kissing Circle]]<br /> <br /> In the diagram above, we see that for a curved motion C, the kissing circle when the object is at point P is shown with the blue circle, where the radius is indicated by the red arrow. Often, there are several types of kissing circles within an object's curving motion, so we have to look at the the instantaneous situation to derive instantaneous values. The tangential straight blue line segways into our next topic, the parallel component of the change in momentum.<br /> <br /> ===Parallel Component and Tangential Properties of Curving Motion===<br /> There are two scenarios of curving motion that we will entertain here, one where an object is not changing speed along its curved path and another where the object speeds up or slows down along this curved path. We will start with the constant speed scenario:<br /> <br /> &lt;math&gt;{\frac{d\vec{p}}{dt}}_{parallel}=\vec(0)&lt;/math&gt;<br /> <br /> When an object's tangential velocity is constant throughout the entire motion, we can say that the parallel component of &lt;math&gt;{\frac{d\vec{p}}{dt}}&lt;/math&gt; is zero, as any change in momentum is solely for altering the direction of the object's momentum as opposed to its magnitude. To understand this in more mathematical terms, the only way the magnitude of a momentum vector can be changed is if some component of the force acting on the object lies in the direction of the objects motion. Otherwise, the net force must be in the perpendicular direction towards the center of the kissing circle, like shown below:<br /> <br /> [[File:Vector-diagram.png|Kissing Circle]]<br /> <br /> Here we see that the tangential velocities indicated by the red arrows are all of the same magnitude, and the only thing altering them is the centripetal acceleration, which leads into our discussion of centripetal and centrifugal forces later. Now we will consider cases where &lt;math&gt;{\frac{d\vec{p}}{dt}}&lt;/math&gt; is nonzero. In these cases, the speed of the object along it's curved path is changing and our net force vector has a component that is parallel to the object's tangential motion.<br /> <br /> ===Calculating &lt;math&gt;{\frac{d\vec{p}}{dt}}_{parallel}&lt;/math&gt; and &lt;math&gt;{\frac{d\vec{p}}{dt}}_{perpendicular}&lt;/math&gt;<br /> Given a instantaneous force acting on the object as well as it's initial momentum, we can calculate the final momentum using the Momentum Principle and then observe any change in magnitude between these two vector quantities. Here, &lt;math&gt;{\frac{d\vec{p}}{dt}}_{parallel}&lt;/math&gt; is equal to the difference between the magnitudes of the initial and final momentum divided by the change in time. From this, we can calculate &lt;math&gt;{\frac{d\vec{p}}{dt}}_{perpendicular}&lt;/math&gt; by subtracting &lt;math&gt;{\frac{d\vec{p}}{dt}}_{parallel}&lt;/math&gt; from the net change in momentum. A glowscript animation utilizing this method is linked below:<br /> <br /> [http://www.glowscript.org/#/user/aayush.kumarmail/folder/Private/program/SpaceVoyageandCurvingMotion Curving Motion with a Satellite Projectile]<br /> <br /> ===Centripetal and Centrifugal Forces===<br /> The Centripetal and Centrifugal Forces of an object in motion demonstrate reciprocity in that the Centripetal Force acts inward towards the center of the kissing circle whereas the centrifugal force is the object's tendency to fly outward.<br /> [[Category:Momentum]]</div>

Akumar http://www.physicsbook.gatech.edu/index.php?title=Curving_Motion&diff=12893 2015-12-05T00:01:56Z

<p>Akumar: </p> <hr /> <div>claimed by Aayush Kumar<br /> <br /> Short Description of Topic:<br /> The momentum of an object is nonconstant when it is traveling along a curved path, regardless of whether or not it's speed along the curve is changing.<br /> ==The Main Idea==<br /> <br /> Such cases of curving motion can be analyzed using the properties of the parallel and perpendicular components of net Force as well as understanding the motion's &quot;Kissing Circle&quot;.<br /> <br /> ==Parallel and Perpendicular Components of &lt;math&gt;{\frac{d\vec{p}}{dt}}&lt;/math&gt;==<br /> <br /> ===Perpendicular Component and the Kissing Circle===<br /> This is perhaps the most crucial element of this topic, as a property of smoothly continuous curving motion is that the perpendicular component of the change in momentum is &lt;math&gt;{\frac{d\vec{p}}{dt}}_{perpendicular}=\frac{m v^{2}}{R}&lt;/math&gt; where m is the mass of the object, v is the magnitude of its velocity, and R is the radius of the kissing circle, which we will explain shortly. In essence, the kissing circle of the object is the imaginary circular arc that it temporarily follows along its curved motion, where the radius is the distance to the center of said imaginary circle.<br /> <br /> [[File:Osculating circle.svg|Kissing Circle]]<br /> <br /> In the diagram above, we see that for a curved motion C, the kissing circle when the object is at point P is shown with the blue circle, where the radius is indicated by the red arrow. Often, there are several types of kissing circles within an object's curving motion, so we have to look at the the instantaneous situation to derive instantaneous values. The tangential straight blue line segways into our next topic, the parallel component of the change in momentum.<br /> <br /> ===Parallel Component and Tangential Properties of Curving Motion===<br /> There are two scenarios of curving motion that we will entertain here, one where an object is not changing speed along its curved path and another where the object speeds up or slows down along this curved path. We will start with the constant speed scenario:<br /> <br /> &lt;math&gt;{\frac{d\vec{p}}{dt}}_{parallel}=\vec(0)&lt;/math&gt;<br /> <br /> When an object's tangential velocity is constant throughout the entire motion, we can say that the parallel component of &lt;math&gt;{\frac{d\vec{p}}{dt}}&lt;/math&gt; is zero, as any change in momentum is solely for altering the direction of the object's momentum as opposed to its magnitude. To understand this in more mathematical terms, the only way the magnitude of a momentum vector can be changed is if some component of the force acting on the object lies in the direction of the objects motion. Otherwise, the net force must be in the perpendicular direction towards the center of the kissing circle, like shown below:<br /> <br /> [[File:Vector-diagram.png|Kissing Circle]]<br /> <br /> Here we see that the tangential velocities indicated by the red arrows are all of the same magnitude, and the only thing altering them is the centripetal acceleration, which leads into our discussion of centripetal and centrifugal forces later. Now we will consider cases where &lt;math&gt;{\frac{d\vec{p}}{dt}}&lt;/math&gt; is nonzero. In these cases, the speed of the object along it's curved path is changing and our net force vector has a component that is parallel to the object's tangential motion.<br /> <br /> ===Calculating &lt;math&gt;{\frac{d\vec{p}}{dt}}_{parallel}&lt;/math&gt; and &lt;math&gt;{\frac{d\vec{p}}{dt}}_{perpendicular}&lt;/math&gt;<br /> Given a instantaneous force acting on the object as well as it's initial momentum, we can calculate the final momentum using the Momentum Principle and then observe any change in magnitude between these two vector quantities. Here, &lt;math&gt;{\frac{d\vec{p}}{dt}}_{parallel}&lt;/math&gt; is equal to the difference between the magnitudes of the initial and final momentum divided by the change in time. From this, we can calculate &lt;math&gt;{\frac{d\vec{p}}{dt}}_{perpendicular}&lt;/math&gt; by subtracting &lt;math&gt;{\frac{d\vec{p}}{dt}}_{parallel}&lt;/math&gt; from the net change in momentum. A glowscript animation utilizing this method is linked below:<br /> <br /> [http://www.glowscript.org/#/user/aayush.kumarmail/folder/Private/program/SpaceVoyageandCurvingMotion Curving Motion with a Satellite Projectile]<br /> <br /> [[Category:Which Category did you place this in?]]</div>

Akumar http://www.physicsbook.gatech.edu/index.php?title=Curving_Motion&diff=12866 2015-12-04T23:49:57Z

<p>Akumar: </p> <hr /> <div>claimed by Aayush Kumar<br /> <br /> Short Description of Topic:<br /> The momentum of an object is nonconstant when it is traveling along a curved path, regardless of whether or not it's speed along the curve is changing.<br /> ==The Main Idea==<br /> <br /> Such cases of curving motion can be analyzed using the properties of the parallel and perpendicular components of net Force as well as understanding the motion's &quot;Kissing Circle&quot;.<br /> <br /> ==Parallel and Perpendicular Components of &lt;math&gt;{\frac{d\vec{p}}{dt}}&lt;/math&gt;==<br /> <br /> ===Perpendicular Component and the Kissing Circle===<br /> This is perhaps the most crucial element of this topic, as a property of smoothly continuous curving motion is that the perpendicular component of the change in momentum is &lt;math&gt;{\frac{d\vec{p}}{dt}}_{perpendicular}=\frac{m v^{2}}{R}&lt;/math&gt; where m is the mass of the object, v is the magnitude of its velocity, and R is the radius of the kissing circle, which we will explain shortly. In essence, the kissing circle of the object is the imaginary circular arc that it temporarily follows along its curved motion, where the radius is the distance to the center of said imaginary circle.<br /> <br /> [[File:Osculating circle.svg|Kissing Circle]]<br /> <br /> In the diagram above, we see that for a curved motion C, the kissing circle when the object is at point P is shown with the blue circle, where the radius is indicated by the red arrow. Often, there are several types of kissing circles within an object's curving motion, so we have to look at the the instantaneous situation to derive instantaneous values. The tangential straight blue line segways into our next topic, the parallel component of the change in momentum.<br /> <br /> ===Parallel Component and Tangential Properties of Curving Motion===<br /> There are two scenarios of curving motion that we will entertain here, one where an object is not changing speed along its curved path and another where the object speeds up or slows down along this curved path. We will start with the constant speed scenario:<br /> <br /> &lt;math&gt;{\frac{d\vec{p}}{dt}}_{parallel}=\vec(0)&lt;/math&gt;<br /> <br /> When an object's tangential velocity is constant throughout the entire motion, we can say that the parallel component of &lt;math&gt;{\frac{d\vec{p}}{dt}}&lt;/math&gt; is zero, as any change in momentum is solely for altering the direction of the object's momentum as opposed to its magnitude. To understand this in more mathematical terms, the only way the magnitude of a momentum vector can be changed is if some component of the force acting on the object lies in the direction of the objects motion. Otherwise, the net force must be in the perpendicular direction towards the center of the kissing circle, like shown below:<br /> <br /> [[File:Vector-diagram.png|Kissing Circle]]<br /> <br /> What are the mathematical equations that allow us to model this topic. For example &lt;math&gt;{\frac{d\vec{p}}{dt}}_{system} = \vec{F}_{net}&lt;/math&gt; where '''p''' is the momentum of the system and '''F''' is the net force from the surroundings.<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>

Akumar http://www.physicsbook.gatech.edu/index.php?title=File:Vector-diagram.png&diff=12863 2015-12-04T23:48:46Z

<p>Akumar: </p> <hr /> <div></div>

Akumar http://www.physicsbook.gatech.edu/index.php?title=Curving_Motion&diff=12825 2015-12-04T23:17:38Z

<p>Akumar: </p> <hr /> <div>claimed by Aayush Kumar<br /> <br /> Short Description of Topic:<br /> The momentum of an object is nonconstant when it is traveling along a curved path, regardless of whether or not it's speed along the curve is changing.<br /> ==The Main Idea==<br /> <br /> Such cases of curving motion can be analyzed using the properties of the parallel and perpendicular components of net Force as well as understanding the motion's &quot;Kissing Circle&quot;.<br /> <br /> ==Parallel and Perpendicular Components of &lt;math&gt;{\frac{d\vec{p}}{dt}}&lt;/math&gt;==<br /> <br /> ===Perpendicular Component and the Kissing <br /> What are the mathematical equations that allow us to model this topic. For example &lt;math&gt;{\frac{d\vec{p}}{dt}}_{system} = \vec{F}_{net}&lt;/math&gt; where '''p''' is the momentum of the system and '''F''' is the net force from the surroundings.<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>

Akumar http://www.physicsbook.gatech.edu/index.php?title=Curving_Motion&diff=535 2015-11-09T00:44:14Z

<p>Akumar: </p> <hr /> <div>claimed by Aayush Kumar<br /> <br /> Short Description of Topic<br /> <br /> ==The Main Idea==<br /> <br /> State, in your own words, the main idea for this topic<br /> Electric Field of Capacitor<br /> <br /> ===A Mathematical Model===<br /> <br /> What are the mathematical equations that allow us to model this topic. For example &lt;math&gt;{\frac{d\vec{p}}{dt}}_{system} = \vec{F}_{net}&lt;/math&gt; where '''p''' is the momentum of the system and '''F''' is the net force from the surroundings.<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>

Akumar http://www.physicsbook.gatech.edu/index.php?title=Curving_Motion&diff=534 2015-11-09T00:41:34Z

<p>Akumar: Force and Curving motion, where dp/dt_perpendicular = mv^2/r and dp/dt_parallel = F_tangential</p> <hr /> <div>claimed by Aayush Kumar</div>

Akumar http://www.physicsbook.gatech.edu/index.php?title=Main_Page&diff=533 2015-11-09T00:39:48Z

<p>Akumar: /* Momentum */</p> <hr /> <div>__NOTOC__<br /> Welcome to the Georgia Tech Wiki for Intro Physics. This resources was created so that students can contribute and curate content to help those with limited or no access to a textbook. When reading this website, please correct any errors you may come across. If you read something that isn't clear, please consider revising it!<br /> <br /> Looking to make a contribution?<br /> #Pick a specific topic from intro physics<br /> #Add that topic, as a link to a new page, under the appropriate category listed below by editing this page.<br /> #Copy and paste the default [[Template]] into your new page and start editing.<br /> <br /> Please remember that this is not a textbook and you are not limited to expressing your ideas with only text and equations. Whenever possible embed: pictures, videos, diagrams, simulations, computational models (e.g. Glowscript), and whatever content you think makes learning physics easier for other students.<br /> <br /> == Source Material ==<br /> All of the content added to this resource must be in the public domain or similar free resource. If you are unsure about a source, contact the original author for permission. That said, there is a surprisingly large amount of introductory physics content scattered across the web. Here is an incomplete list of intro physics resources (please update as needed).<br /> * A physics resource written by experts for an expert audience [https://en.wikipedia.org/wiki/Portal:Physics Physics Portal]<br /> * A wiki book on modern physics [https://en.wikibooks.org/wiki/Modern_Physics Modern Physics Wiki]<br /> * The MIT open courseware for intro physics [http://ocw.mit.edu/resources/res-8-002-a-wikitextbook-for-introductory-mechanics-fall-2009/index.htm MITOCW Wiki]<br /> * An online concept map of intro physics [http://hyperphysics.phy-astr.gsu.edu/hbase/hph.html HyperPhysics]<br /> * Interactive physics simulations [https://phet.colorado.edu/en/simulations/category/physics PhET]<br /> * OpenStax algebra based intro physics textbook [https://openstaxcollege.org/textbooks/college-physics College Physics]<br /> * The Open Source Physics project is a collection of online physics resources [http://www.opensourcephysics.org/ OSP]<br /> * A resource guide compiled by the [http://www.aapt.org/ AAPT] for educators [http://www.compadre.org/ ComPADRE]<br /> <br /> == Organizing Catagories ==<br /> These are the broad, overarching categories, that we cover in two semester of introductory physics. You can add subcategories or make a new category as needed. A single topic should direct readers to a page in one of these catagories.<br /> <br /> &lt;div class=&quot;toccolours mw-collapsible mw-collapsed&quot;&gt;<br /> ===Interactions===<br /> &lt;div class=&quot;mw-collapsible-content&quot;&gt;<br /> *[[Fundamental Interactions]] <br /> *[[System &amp; Surroundings]] <br /> <br /> &lt;/div&gt;<br /> &lt;/div&gt;<br /> <br /> &lt;div class=&quot;toccolours mw-collapsible mw-collapsed&quot;&gt;<br /> <br /> ===Theory===<br /> &lt;div class=&quot;mw-collapsible-content&quot;&gt;<br /> *[[Einstein's Theory of Relativity]]<br /> &lt;/div&gt;<br /> &lt;/div&gt;<br /> <br /> &lt;div class=&quot;toccolours mw-collapsible mw-collapsed&quot;&gt;<br /> <br /> ===Notable Scientists===<br /> &lt;div class=&quot;mw-collapsible-content&quot;&gt;<br /> *[[Albert Einstein]]<br /> &lt;/div&gt;<br /> &lt;/div&gt;<br /> <br /> &lt;div class=&quot;toccolours mw-collapsible mw-collapsed&quot;&gt;<br /> <br /> <br /> ===Properties of Matter===<br /> &lt;div class=&quot;mw-collapsible-content&quot;&gt;<br /> *[[Mass]]<br /> *[[Charge]]<br /> *[[Spin]]<br /> *[[SI Units]]<br /> &lt;/div&gt;<br /> &lt;/div&gt;<br /> <br /> &lt;div class=&quot;toccolours mw-collapsible mw-collapsed&quot;&gt;<br /> <br /> ===Contact Interactions===<br /> &lt;div class=&quot;mw-collapsible-content&quot;&gt;<br /> * [[Young's Modulus]]<br /> * [[Friction]]<br /> * [[Tension]]<br /> &lt;/div&gt;<br /> &lt;/div&gt;<br /> <br /> &lt;div class=&quot;toccolours mw-collapsible mw-collapsed&quot;&gt;<br /> <br /> ===Momentum===<br /> &lt;div class=&quot;mw-collapsible-content&quot;&gt;<br /> * [[Vectors]]<br /> * [[Kinematics]]<br /> * Predicting Change in one dimension<br /> * [[Predicting Change in multiple dimensions]]<br /> * [[Momentum Principle]]<br /> * [[Curving Motion]]<br /> &lt;/div&gt;<br /> &lt;/div&gt;<br /> <br /> &lt;div class=&quot;toccolours mw-collapsible mw-collapsed&quot;&gt;<br /> <br /> ===Angular Momentum===<br /> &lt;div class=&quot;mw-collapsible-content&quot;&gt;<br /> * [[The Moments of Inertia]]<br /> * [[Rotation]]<br /> * [[Torque]]<br /> * Predicting a Change in Rotation<br /> &lt;/div&gt;<br /> &lt;/div&gt;<br /> <br /> &lt;div class=&quot;toccolours mw-collapsible mw-collapsed&quot;&gt;<br /> <br /> ===Energy===<br /> &lt;div class=&quot;mw-collapsible-content&quot;&gt;<br /> *[[Predicting Change]]<br /> *[[Rest Mass Energy]]<br /> *[[Kinetic Energy]]<br /> *[[Potential Energy]]<br /> *[[Work]]<br /> *[[Thermal Energy]]<br /> *[[Conservation of Energy]]<br /> *[[Electric Potential]]<br /> &lt;/div&gt;<br /> &lt;/div&gt;<br /> <br /> &lt;div class=&quot;toccolours mw-collapsible mw-collapsed&quot;&gt;<br /> <br /> ===Fields===<br /> &lt;div class=&quot;mw-collapsible-content&quot;&gt;<br /> * [[Electric Field]] of a<br /> ** [[Point Charge]]<br /> ** [[Electric Dipole]]<br /> ** [[Capacitor]]<br /> ** [[Charged Rod]]<br /> ** [[Charged Disk]]<br /> ** [[Charged Spherical Shell]]<br /> *[[Electric Potential]] <br /> **[[Potential Difference in a Uniform Field]]<br /> *[[Magnetic Field]]<br /> **[[Direction of Magnetic Field]]<br /> **[[Bar Magnet]]<br /> **[[Magnetic Force]]<br /> **[[Hall Effect]]<br /> **[[Lorentz Force]]<br /> **[[Biot-Savart Law]]<br /> **[[Integration Techniques for Magnetic Field]]<br /> **[[Sparks in Air]]<br /> **[[Motional Emf]]<br /> &lt;/div&gt;<br /> &lt;/div&gt;<br /> <br /> &lt;div class=&quot;toccolours mw-collapsible mw-collapsed&quot;&gt;<br /> <br /> ===Simple Circuits===<br /> &lt;div class=&quot;mw-collapsible-content&quot;&gt;<br /> *[[Components]]<br /> *[[Steady State]]<br /> *[[Non Steady State]]<br /> *[[Node Rule]]<br /> *[[Loop Rule]]<br /> *[[Power in a circuit]]<br /> *[[Ammeters,Voltmeters,Ohmmeters]]<br /> *[[Current]]<br /> *[[Ohm's Law]]<br /> &lt;/div&gt;<br /> &lt;/div&gt;<br /> <br /> &lt;div class=&quot;toccolours mw-collapsible mw-collapsed&quot;&gt;<br /> <br /> ===Maxwell's Equations===<br /> &lt;div class=&quot;mw-collapsible-content&quot;&gt;<br /> *[[Gauss's Flux Theorem]]<br /> **[[Electric Fields]]<br /> **[[Magnetic Fields]]<br /> *[[Faraday's Law]]<br /> **[[Inductance]]<br /> *[[Ampere-Maxwell Law]]<br /> &lt;/div&gt;<br /> &lt;/div&gt;<br /> <br /> &lt;div class=&quot;toccolours mw-collapsible mw-collapsed&quot;&gt;<br /> <br /> ===Radiation===<br /> &lt;div class=&quot;mw-collapsible-content&quot;&gt;<br /> &lt;/div&gt;<br /> &lt;/div&gt;<br /> <br /> == Resources ==<br /> * Commonly used wiki commands [https://en.wikipedia.org/wiki/Help:Cheatsheet Wiki Cheatsheet]<br /> * A guide to representing equations in math mode [https://en.wikipedia.org/wiki/Help:Displaying_a_formula Wiki Math Mode]<br /> * A page to keep track of all the physics [[Constants]]<br /> * An overview of [[VPython]]</div>

Akumar