A.4.9 (HL)—Angular momentum

Rotational momentum

For a rigid body rotating about a fixed axis,

$$L=I\omega$$

Angular momentum is directed along the rotation axis by the right-hand convention.

Use the matching inertia

The moment of inertia must be calculated about the same axis used for $L$. A larger $I$ at the same angular speed means larger angular momentum.

Worked example from local Question Bank row 31945

For $I=450\,\mathrm{kg\,m^2}$ and $\omega=1.66\,\mathrm{rad\,s^{-1}}$,

$$L=I\omega=(450)(1.66)=7.47\times10^2\,\mathrm{kg\,m^2\,s^{-1}}\approx750\,\mathrm{kg\,m^2\,s^{-1}}$$

The sign or axis direction must match the chosen rotational convention.

Common trap

Do not substitute translational momentum $mv$ for angular momentum when the question describes rotation.