The method and the results are on the angular momentum lab. Do the analysis yourself first, then check the answers below.
Quick answer: Angular momentum is L = Iω, and it stays constant when no net external torque acts, so a spinner who pulls mass inward spins faster. These answers go with the AP Physics 1 lab on angular momentum: the graph, the calculations, the uncertainties and the conclusion explained, for all 8 analysis questions.
The model answers use the sample data above. Your own rotational inertia will differ, but the angular momentum before and after should agree closely, while the kinetic energy increases.
Level: AP Physics 1 (algebra-based) · Curriculum: AP P1 Unit 6
Question 1 Angular speeds
Arms out: ω = 18.85 ÷ 17.2 = 1.10 rad/s. Arms in: ω = 18.85 ÷ 10.0 = 1.89 rad/s (3 turns = 6π = 18.85 rad).
Question 2 Rotational inertia of the weights
Out: 2 × 1.5 × (0.70)² = 1.47 kg m². In: 2 × 1.5 × (0.25)² = 0.19 kg m² (0.1875).
Question 3 Rotational inertia of student and chair
(I0 + 1.47) × 1.096 = (I0 + 0.1875) × 1.885. Expanding: 1.096I0 + 1.611 = 1.885I0 + 0.353, so 0.789I0 = 1.258 and I0 = 1.6 kg m².
Question 4 Checking the conservation law
Out: L = (1.6 + 1.47) × 1.096 = 3.07 × 1.096 = 3.36 kg m²/s. In: L = (1.6 + 0.19) × 1.885 = 1.79 × 1.885 = 3.37 kg m²/s. The difference is about 0.3 %, so L is conserved to within the precision of the measurements.
Question 5 Kinetic energy change
Out: K = ½ × 3.07 × (1.096)² = 1.84 J. In: K = ½ × 1.79 × (1.885)² = 3.18 J. K increases by about 1.3 J because the student does work pulling the weights inwards; L, not K, is conserved.
Question 6 Uncertainty
Range = 17.4 − 17.0 = 0.4 s, so uncertainty = 0.2 s, which is 0.2 ÷ 17.2 = 1.2 %. Since ω ∝ 1/t, ω has the same percentage uncertainty, about 0.013 rad/s.
Question 7 Friction and other errors
Friction in the bearing exerts an external torque, which slowly reduces L, so ω falls between the two measurements and the calculated I0 is distorted. The arms and the weights are not point masses at a single radius, so the weights’ I is slightly different from 2mr². Both make the conservation check slightly imperfect.
Question 8 Making the test fairer
Choose a ball-bearing turntable so that bearing friction is smaller, and time more turns for each reading while filming from above, so the angle against time is known more exactly. These reduce friction and random timing error.
