Explicit physics instruction
Angular momentum for a rigid body can be modeled as L=Iω. Moment of inertia I depends on how mass is distributed relative to the axis.
When net external torque is negligible, total angular momentum is conserved. If I decreases, ω must increase so the product remains constant.
The analogy with linear momentum is useful but not identical: torque changes angular momentum just as external force/impulse changes linear momentum.
Core relation: L=Iω and ΔL=τ_extΔt.
Worked example
A rotating system has I=4 kg·m² and ω=2 rad/s, so L=8 kg·m²/s. If I decreases to 2 kg·m² with negligible external torque, ω rises to 4 rad/s.
Guided question
Why does moving mass farther from the axis generally increase moment of inertia?
Independent work
- Solve three angular-momentum or torque-time problems.
- Declare the system and external-torque assumption.
- Record one unit/assumption check.
Misconception check
Conserved angular momentum does not mean angular speed is constant; I can change.
Formative check
If I is halved with L conserved, what happens to ω?
Reveal response
It doubles.
Mentor evidence conference
Ask Archaemenes to audit the system boundary, moment-of-inertia reasoning, and external-torque claim.
Teacher guidance
Foundation: Compute L=Iω.
Core: Solve conservation and torque-time changes.
Extended: Evaluate conservation residuals with uncertainty.