Angular Momentum: Particles, Systems, and Rigid Bodies

All flashcards

Particle angular momentum

About a specified origin, it is the cross product of position and linear momentum: $\vec l=\vec r\times\vec p$.

Angular momentum of a particle system

It is the vector sum of the particles’ angular momenta about the same origin: $\vec L=\sum_i(\vec r_i\times\vec p_i)$.

Torque and angular momentum

The net torque about a specified origin equals the time rate of change of angular momentum: $\sum\vec\tau=d\vec L/dt$.

Moment of inertia

For discrete mass elements about an axis, $I=\sum_i\Delta m_iR_i^2$, where $R_i$ is each element’s perpendicular distance from the axis.

Angular momentum conservation

When net external torque is zero, a system’s total angular momentum remains constant.

Quiz questions

1. For a system of particles measured about one origin, how is total angular momentum calculated?Answer: $\vec L=\sum_i(\vec r_i\times\vec p_i)$
2. What determines the rate of change of a system’s total angular momentum about a specified origin?Answer: The net external torque about that origin.
3. For a rigid body rotating about a symmetry axis, what relation gives the magnitude of angular momentum?Answer: $L=I\omega$
4. For discrete mass elements rotating about an axis, how is moment of inertia calculated?Answer: $I=\sum_i\Delta m_iR_i^2$
5. For a rigid body with constant moment of inertia rotating about a fixed axis, what is the net torque?Answer: $\sum\tau=I\alpha$