Angular Momentum: Definitions, Inertia, and Conservation

All flashcards

Angular momentum of a particle

The rotational analogue of linear momentum, defined relative to an origin by $\mathbf{L}=\mathbf{r}\times\mathbf{p}$.

Direction of angular momentum

For a particle, it is perpendicular to both $\mathbf{r}$ and $\mathbf{p}$; use the right-hand rule to find its direction.

Moment arm

The perpendicular distance from an origin to a particle's line of motion; angular momentum magnitude is $L=r_{\perp}p$.

Orbital angular momentum

Angular momentum measured about a chosen external point or center.

Spin angular momentum

Angular momentum measured about an object's own center of mass.

Quiz questions

1. What condition conserves a system's total angular momentum?Answer: The net external torque on the system is zero.
2. How is net torque related to angular momentum?Answer: It equals the time rate of change of angular momentum.
3. Why does a central force produce zero torque about its center?Answer: The force is parallel or antiparallel to the position vector.
4. How does Noether's theorem connect angular momentum conservation to symmetry?Answer: Rotational symmetry of the laws implies conservation of angular momentum.
5. What distinguishes spin angular momentum from orbital angular momentum?Answer: Spin is measured about the center of mass; orbital momentum is measured about an external point.