Angular Momentum, Equilibrium and Rolling Motion

Name: Angular Momentum, Equilibrium and Rolling Motion
Author: StemPy Lab

A skater pulls in her arms and spins faster. A ladder stays at rest against a wall. A disc rolls down a slope and beats a ring. In this course we define angular momentum and use its conservation, we write the two conditions of equilibrium of a rigid body to solve problems on beams and ladders, and we study rolling motion, its kinetic energy and its motion on an inclined plane.

3 lessons, about 1 h 15 min3 simulations12 problems6 practice questionsPython in every lesson

Created by StemPy Lab

Course outline (3 lessons)

Lesson 1about 25 min
Angular momentum and its conservation
Angular momentum is $\vec{L} = \vec{r} \times \vec{p}$ for a particle, and $L = I\omega$ for a body turning about a fixed axis. Torque is its rate of change: $\vec{\tau} = \dfrac{d\vec{L}}{dt}$ . With no external torque, angular momentum is conserved, so a body that pulls its mass inward spins faster. Its kinetic energy $\dfrac{L^2}{2I}$ then grows, paid for by the work of pulling in.
1 simulation2 practice questions1 Python program4 problems1 Python lab1 question set
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Lesson 2about 25 min
Equilibrium of a rigid body
A rigid body is in equilibrium when the net external force is zero (no acceleration of the centre of mass) and the net torque about every point is zero (no angular acceleration). In practice: balance the forces along two axes, and take torques about a well-chosen point, often where an unknown force acts. A couple, two equal and opposite forces not along one line, has zero net force but a torque.
1 simulation2 practice questions1 Python program4 problems1 Python lab
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Lesson 3about 25 min
Rolling motion
Rolling without slipping is moving along at $v$ plus turning at $\omega = \dfrac{v}{R}$ : the point touching the ground is at rest, the top moves at $2v$ . Its kinetic energy is $\tfrac12 Mv^2 + \tfrac12 I\omega^2 = \tfrac12 Mv^2\left(1 + \dfrac{I}{MR^2}\right)$ . Down a slope, $a = \dfrac{g\sin\theta}{1 + I/MR^2}$ : a solid ball beats a disc, which beats a ring, whatever their sizes.
1 simulation2 practice questions1 Python program4 problems1 Python lab1 note
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Angular Momentum, Equilibrium and Rolling: Practice Paper

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Angular Momentum, Equilibrium and Rolling Motion

Course outline (3 lessons)

Angular momentum and its conservation

Equilibrium of a rigid body

Rolling motion

Test Your Learning

Your teacher

Discussion (0)