Centre of Mass and the Motion of a System

Name: Centre of Mass and the Motion of a System
Author: StemPy Lab

A shell bursts in the air into many pieces, but one point of the pieces still follows the smooth path of the shell. In this course we find the centre of mass of a system, we see why only the external forces move it, we use it to solve problems of boats, skaters and bursting shells, and we describe the turning of a rigid body with angular velocity and angular acceleration.

3 lessons, about 1 h 10 min3 simulations12 problems6 practice questionsPython in every lesson

Created by StemPy Lab

Course outline (3 lessons)

Lesson 1about 25 min
The centre of mass of a system of particles
The centre of mass is the mass-weighted average position of a system: $\vec{r}_{cm} = \dfrac{\sum m_i\vec{r}_i}{\sum m_i}$ . It lies nearer the heavier parts, at the centre of a uniform symmetric body, and possibly where there is no material at all. A body with a piece removed can be handled by treating the hole as a negative mass.
1 simulation2 practice questions1 Python program4 problems1 question set
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Lesson 2about 25 min
Motion of the centre of mass and the momentum of a system
The centre of mass of a system moves as if all the mass were there and all the external forces acted on it: $M\vec{a}_{cm} = \vec{F}_{\text{ext}}$ . Internal forces cannot move it. The total momentum is $\vec{P} = M\vec{v}_{cm}$ , so with no external force the centre of mass keeps a steady velocity, however the parts move.
1 simulation2 practice questions1 Python program4 problems1 Python lab
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Lesson 3about 20 min
Rigid bodies, angular velocity and the kinematics of rotation
A rigid body keeps the distances between its particles fixed. In rotation about a fixed axis, every particle turns through the same angle, so all share one angular velocity $\omega = \dfrac{d\theta}{dt}$ and one angular acceleration $\alpha = \dfrac{d\omega}{dt}$ . With steady $\alpha$ , the equations of rotation copy the equations of motion: $\omega = \omega_0 + \alpha t$ , $\theta = \omega_0t + \tfrac12\alpha t^2$ , $\omega^2 = \omega_0^2 + 2\alpha\theta$ . A particle at distance $r$ moves at $v = \omega r$ .
1 simulation2 practice questions1 Python program4 problems1 Python lab1 note
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Centre of Mass and Rigid Body Rotation: Practice Paper

15 questions · 20 min

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More onMechanics › Rotational Motion Mechanics › Momentum and Collisions

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Centre of Mass and the Motion of a System

Course outline (3 lessons)

The centre of mass of a system of particles

Motion of the centre of mass and the momentum of a system

Rigid bodies, angular velocity and the kinematics of rotation

Test Your Learning

Your teacher

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