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# Classical Angular Momentum

## Prerequisites

Students should be able to:

## In-class Content

- Add Angular Momentum SWBQs
- Introduction of Angular Momentum (Lecture, 25 minutes)
- Central Forces on an Air Table (Small Whiteboard Activity, 15 minutes)
- RESOURCE: Spherical coordinates handout showing unit vectors.

## Homework for Central Forces

- (CentralForce)
*Determine whether several common forces in nature are central forces.*Which of the following forces can be central forces? which cannot?

The force on a test mass $m$ in a gravitational field $\Vec{g }$, i.e. $m\Vec g$

The force on a test charge $q$ in an electric field $\Vec E$, i.e. $q\Vec E$

The force on a test charge $q$ moving at velocity $\Vec{v }$ in a magnetic field $\Vec B$, i.e. $q\Vec v \times \Vec B$

- (FreeCentralForce)
*A simple check on your understanding of center-of-mass motion.*If a central force is the only force acting on a system of two masses (i.e. no external forces), what will the motion of the center of mass be?

- (PlanarOrbit)
*A simple check on your understanding of classical angular momentum.*}Show that the plane of the orbit is perpendicular to the angular momentum vector $\Vec L$.

- (CMLandT)
*Explicitly show how the kinetic energy and angular momentum of a two particle system is related to the energy and angular momentum of the center of mass and reduced mass system.*Consider a system of two particles.

Show that the total kinetic energy of the system is the same as that of two “fictitious” particles: one of mass $M=m_1+m_2$ moving with the speed of the CM (center of mass) and one of mass $\mu$ (the reduced mass) moving with the speed of the relative position $\vec{r}=\vec{r}_2-\vec{r}_1$.

Show that the total angular momentum of the system can be similarly decomposed into the angular momenta of these two fictitious particles.