Mistake Master

Angular Momentum and Angular Impulse

▶︎  Watch it animatedinteractive step-through · ~3 min · optional

A torque acting over time changes a body's angular momentum. When that torque varies in time, the change is not τ times the elapsed time. It is the area under the τ-vs-t curve: ΔL = ∫ τ dt. The momentum itself is L = r × p for a particle; for a rigid body spinning about a fixed axis it becomes L = I ω.

ANGULAR MOMENTUM & IMPULSE ΔL = ∫ τ dt Angular impulse is the area under the torque in time. L ω F τ over time changes L = I ω t τ τ Δt ΔL = area impulse : area under τ-vs-t = ΔL momentum : L = r × p = I ω
A torque acting over time changes a body's angular momentum. When τ varies with t, the angular impulse is the area under the τ-vs-t curve, ΔL = ∫ τ dt, not the constant-torque rectangle τ Δt. Below the axis the area is negative: a braking torque lowers L.
The angular impulse under the torque · Open the sandbox →

Topic 6.3 is the time twin of 6.2: there you integrated torque over angle for the work; here you integrate it over time for the change in angular momentum. The slips are calculus and vector ones: using τ Δt when τ varies, confusing the impulse with the work, mismatching the partners in L = I ω, dropping the sine in r p sin θ, or losing the direction from the right-hand rule.

Angular impulse

3 ways in · any order
Lesson
Angular Momentum and Angular Impulse

Angular momentum L = r cross p = I omega and angular impulse as the area under the torque in time, delta L = integral of tau dt. Covers when the constant-torque shortcut tau delta-t fails, angular impulse versus work, the cross-product magnitude r p sin theta, and the right-hand-rule direction. Closes with a ten-scenario skill check.

Skill check · 10 scenarios
Diagnostic
10-item topic check

Ten items across the five Topic 6.3 mistakes: using tau delta-t for a torque that varies, confusing angular impulse with work, mismatching the partners in L = I omega, taking the cross-product magnitude without the sine, and losing the direction or sign of the angular momentum. Take it cold to see what still trips you up, or after the lesson to confirm it doesn't.

Not started · 10 items · ~15 min
Targeted Practice
Drill a single misconception

Pick one mistake you keep making and drill it on its own. Two correct in a row clears it and you move on.

Take the diagnostic to identify your misconceptions