Physics HL · Chapter 5: Rigid Body Mechanics
5.5 Angular Momentum and Conservation
Use angular momentum and angular impulse to reason about rotational change and conserved behavior.
Estimated time: 18 minutes
Angular Momentum for Rigid Rotation
For a rigid body about a fixed axis, angular momentum scales with inertia and angular speed.
Angular momentum plays for rotation the same structural role that linear momentum plays for translation. A larger moment of inertia at the same angular speed means larger angular momentum, and a faster spin at fixed inertia does the same.
Torque, Angular Impulse, and Change in L
Net torque changes angular momentum; applied over time, it gives angular impulse.
If external net torque is approximately zero, angular momentum remains constant. This is why skaters spin faster when pulling arms inward: reducing I requires omega to increase so that L stays the same.
Chapter 5 Wrap-Up
A complete rigid body solution often combines all chapter ideas. Start with geometry and axes, compute torques and force balance, select either dynamics or energy methods, and finish with momentum conservation when external torques are negligible. This layered method is more reliable than memorizing isolated formulas.
Rigid Body Mechanics Checklist
- Always define axis and sign convention before writing tau equations.
- For static cases, satisfy both sum F = 0 and sum tau = 0.
- Use tau_net = I alpha when rotational acceleration is required.
- For rolling without slipping, enforce v_cm = omega R with either energy or dynamics.
- If external net torque is zero, apply angular momentum conservation.