Center of Mass - Revision history

YorickAndeweg at 00:18, 6 August 2019

2019-08-06T00:18:11Z

← Older revision		Revision as of 20:18, 5 August 2019
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	<!--If you are editing this page:		<!--If you are editing this page:
	1) consider changing the definition to average position of all the matter in the system		1) consider changing the definition to average position of all the matter in the system
	2) consider talking about how to calculate center of mass for point mass systems as well as 3D mass distributions-->		2) consider talking about how to calculate center of mass for point mass systems as well as 3D mass distributions
			3) consider talking about some of its properties, such as the fact that free-floating objects can rotate only about their COM without external force
			-->

	==The Main Idea==		==The Main Idea==

YorickAndeweg at 00:15, 6 August 2019

2019-08-06T00:15:16Z

← Older revision		Revision as of 20:15, 5 August 2019
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			<!--If you are editing this page:
			1) consider changing the definition to average position of all the matter in the system
			2) consider talking about how to calculate center of mass for point mass systems as well as 3D mass distributions-->

	==The Main Idea==		==The Main Idea==

Parkercoye: /* A Computational Model */

2019-07-29T15:31:30Z

A Computational Model

← Older revision		Revision as of 11:31, 29 July 2019
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	Center of mass can be a powerful tool for simplifying problems in physics. Similarly, using VPython (or any other programming language, for that matter), using concepts related to center of mass can greatly simplify code. Simply finding the center of mass of a virtual object can be very simple for an object with uniform mass and volume, however if that is changing, an iterative process for finding center of mass may need to be implemented.		Center of mass can be a powerful tool for simplifying problems in physics. Similarly, using VPython (or any other programming language, for that matter), using concepts related to center of mass can greatly simplify code. Simply finding the center of mass of a virtual object can be very simple for an object with uniform mass and volume, however if that is changing, an iterative process for finding center of mass may need to be implemented.

	For more information on iteration and coding, visit this page [[~~Center of Mass~~]]. It is an important concept in this course and is one very easily adapted to center of mass concepts.		For more information on iteration and coding, visit this page: [[VPython Loops]]. It is an important concept in this course and is one very easily adapted to center of mass concepts.

	===Velocity, Momentum, and Kinetic Energy with Center of Mass===		===Velocity, Momentum, and Kinetic Energy with Center of Mass===

Parkercoye: /* A Computational Model */

2019-07-29T15:29:43Z

A Computational Model

← Older revision		Revision as of 11:29, 29 July 2019
Line 28:		Line 28:
	Center of mass can be a powerful tool for simplifying problems in physics. Similarly, using VPython (or any other programming language, for that matter), using concepts related to center of mass can greatly simplify code. Simply finding the center of mass of a virtual object can be very simple for an object with uniform mass and volume, however if that is changing, an iterative process for finding center of mass may need to be implemented.		Center of mass can be a powerful tool for simplifying problems in physics. Similarly, using VPython (or any other programming language, for that matter), using concepts related to center of mass can greatly simplify code. Simply finding the center of mass of a virtual object can be very simple for an object with uniform mass and volume, however if that is changing, an iterative process for finding center of mass may need to be implemented.

	For more information on iteration and coding, visit this page. It is an important concept in this course and is one very easily adapted to center of mass concepts.		For more information on iteration and coding, visit this page [[Center of Mass]]. It is an important concept in this course and is one very easily adapted to center of mass concepts.

	===Velocity, Momentum, and Kinetic Energy with Center of Mass===		===Velocity, Momentum, and Kinetic Energy with Center of Mass===

Parkercoye: /* A Computational Model */

2019-07-29T15:29:04Z

A Computational Model

← Older revision		Revision as of 11:29, 29 July 2019
Line 26:		Line 26:

	===A Computational Model===		===A Computational Model===
			Center of mass can be a powerful tool for simplifying problems in physics. Similarly, using VPython (or any other programming language, for that matter), using concepts related to center of mass can greatly simplify code. Simply finding the center of mass of a virtual object can be very simple for an object with uniform mass and volume, however if that is changing, an iterative process for finding center of mass may need to be implemented.

			For more information on iteration and coding, visit this page. It is an important concept in this course and is one very easily adapted to center of mass concepts.

	===Velocity, Momentum, and Kinetic Energy with Center of Mass===		===Velocity, Momentum, and Kinetic Energy with Center of Mass===

Parkercoye: /* Difficult */

2019-07-27T21:36:01Z

Difficult

← Older revision		Revision as of 17:36, 27 July 2019
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	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.		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.

	[[File:~~Continuous_mass_COM_2~~.png\|~~200px~~]]		[[File:pole_2.png\|400px]]

	====Solution====		====Solution====

Parkercoye: /* Difficult */

2019-07-27T21:34:46Z

Difficult

← Older revision		Revision as of 17:34, 27 July 2019
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	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:		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:

	[[File:~~Continuous_mass_COM_soln1~~.png\|~~200px~~]]		[[File:int_3.png\|500px]]

	Therefore, the center of mass lies at L/2, which agrees with the rule of symmetry for uniform masses.		Therefore, the center of mass lies at L/2, which agrees with the rule of symmetry for uniform masses.

Parkercoye: /* Solution */

2019-07-27T21:33:04Z

Solution

← Older revision		Revision as of 17:33, 27 July 2019
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	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:		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:

	[[File:~~2D_COM_SOLN1~~.png\|300px]]		[[File:xcm.png\|300px]]

	Therefore, the center of mass lies 16/15 m from the origin in the x direction.		Therefore, the center of mass lies 16/15 m from the origin in the x direction.
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	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:		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:

	[[File:~~2D_COM_SOLN2~~.png\|300px]]		[[File:ycm.png\|300px]]

	Therefore, the center of mass lies 4/3 m from the origin in the y direction.		Therefore, the center of mass lies 4/3 m from the origin in the y direction.

Parkercoye: /* Moderate */

2019-07-27T21:32:49Z

Moderate

← Older revision		Revision as of 17:32, 27 July 2019
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	3 point masses are placed on the x-y plane as shown:		3 point masses are placed on the x-y plane as shown:

	[[File:redballs_2\|~~300px~~]]		[[File:redballs_2.png\|500px]]

	Find the center of mass. This is an example of a 2-dimensional center of mass problem.		Find the center of mass. This is an example of a 2-dimensional center of mass problem.

Parkercoye: /* Moderate */

2019-07-27T21:31:04Z

Moderate

← Older revision		Revision as of 17:31, 27 July 2019
Line 81:		Line 81:
	3 point masses are placed on the x-y plane as shown:		3 point masses are placed on the x-y plane as shown:

	[[File:~~2D_COM.png~~\|300px]]		[[File:redballs_2\|300px]]

	Find the center of mass. This is an example of a 2-dimensional center of mass problem.		Find the center of mass. This is an example of a 2-dimensional center of mass problem.