# Classical Angular Momentum

## Prerequisites

Students should be able to:

## Homework for Central Forces

1. (CentralForce) Determine whether several common forces in nature are central forces.

Which of the following forces can be central forces? which cannot?

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

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

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

2. (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?

3. (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 $\Vec L$.

4. (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.

1. 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 $\vec{r}=\vec{r}_2-\vec{r}_1$.

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

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