Choose a system before conserving angular momentum
You will be able to: Identify internal interactions and external angular impulse about a specified axis.
When can angular momentum stay constant during a collision?
Two coaxial wheels rub against each other. Friction slows one and speeds the other. For either wheel alone, friction is external. For the two-wheel system, those paired friction torques transfer angular momentum internally.
A useful starting point: Torque–time area changes angular momentum →
Words and symbols before equations
- System boundary
- The objects included in the system you analyze.
- Internal torque pair
- Opposite torques from an interaction between included objects.
- External angular impulse
- Net external torque accumulated over the interval.
- Conservation condition
- Total L is constant throughout an interval when net external torque is zero throughout it.
What this picture assumes
Initial L_A=8 and L_B=2 kg·m²/s. Internal friction transfers 3 from A to B. The external impulse acts on A only. All quantities refer to one shared axis.
Connect the picture to the physics
State the objects, the reference axis and the time interval before using conservation. Compute all angular momenta about the same axis. For the two-wheel system, internal angular impulses cancel, leaving ΔL_system equal to external angular impulse.
An axle can exert a force and still produce zero torque about that axle if its force line passes through the axis. This is why linear momentum need not be conserved when angular momentum about a fixed axle is conserved. Negligible axle friction is an explicit assumption, not an automatic fact.
A nonzero external torque transfers angular momentum between the selected system and its surroundings. Zero net external impulse over an entire interval can give equal initial and final L even if L varied in between; constant L throughout requires zero net torque throughout.
A worked example, step by step
Wheel A starts with L=+8 and B with L=+2 kg·m²/s. During contact, internal friction transfers 3 kg·m²/s from A to B. An external brake gives A an additional −1 kg·m²/s impulse. Find the final values.
- For A, ΔL=−3−1=−4, so L_Af=4 kg·m²/s.
- For B, ΔL=+3, so L_Bf=5 kg·m²/s.
- Combined L changes from 10 to 9 kg·m²/s.
- The internal transfer cancels; the −1 external impulse accounts for the full system change.
An interaction is internal only if both interacting objects are inside your chosen boundary.
Friction acts between two included wheels. Does it necessarily change their total L?
Compare with an explanation
No. That internal interaction transfers equal opposite angular impulses; external torque controls the combined total.
Predict. Change one thing. Explain.
Keep the internal transfer fixed at 3 kg·m²/s and vary the external angular impulse. Explain each wheel’s change, then compare their sum. Identify the setting where the pair retains its initial total L.
On narrow screens, swipe or scroll diagrams sideways to read all labels.
Internal transfer: A loses 3, B gains 3 kg·m²/s. External impulse=-1 kg·m²/s. Final L_A=4, L_B=5; total=9 kg·m²/s. Total change equals external impulse.
Initial L_A=8 and L_B=2 kg·m²/s. Internal friction transfers 3 from A to B. The external impulse acts on A only. All quantities refer to one shared axis.
Explain what you noticed: Which quantity changed? Which stayed fixed? Use the relevant physical relationship or contact condition to justify your prediction.
Apply the idea to a fresh problem Practice →Show what you understand.
Two original questions are a starting check, not proof of mastery. Explain your choice before revealing the answer.
Original written challenge
4 points · self-check · not an official AP questionTwo wheels initially have L values +6 and +1 kg·m²/s. Internal friction transfers 2 from the first to the second, while external impulse on the first is −1. (a) Find each final L. (b) Find initial and final total L. (c) Identify the internal interaction. (d) Explain why conservation fails for the two-wheel system over this interval.
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Compare with the answer and four-point rubric
- 1 point: First: 6−2−1=3; second: 1+2=3 kg·m²/s.
- 1 point: Initial 7; final 6 kg·m²/s.
- 1 point: The friction interaction between the included wheels is internal.
- 1 point: Net external impulse is −1 kg·m²/s, so the system transfers that angular momentum to its surroundings.
Accept equivalent correct methods and explanations. This is a Refresh Kid teaching rubric, not an official AP scoring guideline.
Retrieve it before you reveal it.
RECALL 1What should you specify before conserving L?
Objects, axis, interval and external-torque assumptions.
RECALL 2Does zero external force follow from zero external torque?
No; a force through the axis has zero torque about it.
RECALL 3Can equal endpoint L values hide changes in between?
Yes, if positive and negative external impulses cancel over the interval.
Revisit these tomorrow and a week later. Try a fresh problem and explain why the method applies.
Choose a system before conserving angular momentum
- L_system=ΣL_parts about one axis.
- ΔL_system=external angular impulse; zero external torque maintains constant L.
Remember: An interaction is internal only if both interacting objects are inside your chosen boundary.
Conditions: Initial L_A=8 and L_B=2 kg·m²/s. Internal friction transfers 3 from A to B. The external impulse acts on A only. All quantities refer to one shared axis.
Refresh Kid · Unit 6 · Objectives 6.4.A, 6.4.B · Review edition
Framework, scope and review status
Mapped to College Board CED, Topic 6.4, objectives 6.4.A, 6.4.B. CED effective Fall 2024, current PDF ©2026; checked September 16, 2026. Fall-2026 corrections also checked. The lesson breakdown and questions are original Refresh Kid work, not official topic subdivisions.
Implementation and automated checks are separate from independent teacher review and observation of students. Both human review stages remain pending. This is a review edition, not a certified or validated assessment.
Optional further resource: College Board’s released questions and scoring guides. Papers can combine units; this link is an archive, not an assignment of every question to this lesson.
Our learn, explore, practice and recall sequence is informed by the IES learning guide. The exact Refresh Kid implementation has not been evaluated for learning effectiveness.
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