Rotation & Angular Dynamics · Physics

If net external torque is zero, angular momentum stays constant.

Conservation of angular momentum is one of the most powerful shortcuts in mechanics. The key is choosing the system and the axis so that external torques are truly negligible.

This topic

Conservation of Angular Momentum

Learn when L is conserved, how to choose the right axis, and how to solve classic “changing I” situations.

Condition

When angular momentum is conserved

Angular momentum changes only when there is a net external torque about the axis you care about. If that torque is zero (or negligible), L is constant.

Core condition: Στ_ext = 0 about the chosen axis
Pick the system: what’s “inside” vs “outside”
Pick the axis: conservation can depend on axis choice
Impulse-like torques: short-time events

Mechanism

Changing I changes ω

For rotation about a fixed axis, L = Iω. If L is conserved and I changes, ω must change inversely to keep the product constant.

Fixed-axis form: L = Iω (about that axis)
Decrease I → increase ω (spin faster)
Increase I → decrease ω (spin slower)
Why energy is not necessarily conserved

Examples

Classic conservation scenarios

Skaters pulling in arms, turntables with added masses, and rotating platforms all showcase conservation of angular momentum when external torques are negligible.

Spinning skater: arms in/out
Turntable + person stepping on/off (idealized)
Masses sliding radially on a rotating disk
Collisions where objects stick and rotate together (preview)

Pitfalls

Choosing system and axis correctly

Conservation is powerful but easy to misuse. The most common errors are ignoring external torques that are not actually negligible or switching axes mid-solution.

Friction torques: when can you ignore them?
Support forces can create torque about some axes
Axis must be the same “before and after”
State assumptions explicitly (short time, smooth bearings)

Practice

Practice & Exercises

Practice deciding whether L is conserved, applying L_before = L_after, and interpreting changes in ω when I changes.

Decide if Στ_ext ≈ 0 about an axis
Fixed-axis problems using L = Iω
Skater/turntable style before–after problems
Compare angular momentum vs energy outcomes
Exam-style angular momentum conservation sets