Chapter 6 / Rotational Motion
Angular-momentum comparison: worked answer
Why diagram C has the largest magnitude
Which diagram has the largest angular-momentum magnitude when the magnitudes of r and p are fixed?
Diagram C. Its position and momentum directions are perpendicular, giving the maximum magnitude L = rp.
- For the fixed magnitudes in the prompt, compare L = rp |sinθ|. The angle between the two directions supplies the only changing factor.
- In C, θ = 90° and |sinθ| = 1. This is the largest possible value, so C has the largest angular-momentum magnitude.
- A and B have oblique directions, so |sinθ| is less than 1. D has opposite directions, θ = 180°, so its angular-momentum magnitude is zero. Drawn vector lengths do not override the fixed magnitudes specified in the prompt.
Scoring criteria
- Use L = rp |sinθ| with the fixed r and p magnitudes, rather than comparing drawn arrow lengths.
- Select C and justify the perpendicular-angle maximum; recognize that D's opposite directions give zero.
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Clarified wording and original source
The original wording calls the vectors constant while the diagrams change their relative directions. The comparison holds their magnitudes fixed and varies the angle.
The original prompt remains in the preserved source:
AP source clause (College Board) · Original companion solution