Angular Momentum and Angular Impulse AP Physics 1 FRQ – Exam Style Questions etc.
Angular Momentum and Angular Impulse AP Physics 1 FRQ
Unit 6: Energy and Momentum of Rotating Systems
Weightage : 10-15%
Exam Style Practice Questions,Angular Momentum and Angular Impulse AP Physics 1 FRQ
Question
A pulley of radius R1 and rotational inertia I1 is mounted on an axle with negligible friction. A light cord passing over the pulley has two blocks of mass m attached to either end, as shown above. Assume that the cord does not slip on the pulley. Determine the answers to parts a. and b. in terms of m, R1, I1, and fundamental constants.
a. Determine the tension T in the cord.
b. One block is now removed from the right and hung on the left. When the system is released from rest, the three blocks on the left accelerate downward with an acceleration g/3 . Determine the following.
i. The tension T3 in the section of cord supporting the three blocks on the left
ii. The tension Tl in the section of cord supporting the single block on the right
iii. The rotational inertia I1 of the pulley
c. The blocks are now removed and the cord is tied into a loop, which is passed around the original pulley and a
second pulley of radius 2R1 and rotational inertia 16I1. The axis of the original pulley is attached to a motor that
rotates it at angular speed ω1, which in turn causes the larger pulley to rotate. The loop does not slip on the
pulleys. Determine the following in terms of I1, RI, and ω1.
i. The angular speed ω2 of the larger pulley
ii. The angular momentum L2 of the larger pulley
iii. The total kinetic energy of the system
Answer/Explanation
Ans:
a. 
\(\sum\)F = ma = 0 so T = 2mg
b. i. 
\(\sum F\) = ma
3mg – T3 = 3m(g/3)
T3 = 2mg
ii. 
\(\sum F\) = ma
T1 – mg = m(g/3)
T1 = 4mg/3
iii. \(\sum\)τ = (T3 – T1)R1 = Iα and α = a/R1 = g/3R1
(2mg – 4mg/3)R1 = I1(g/3R1)
I1 = 2mR12
c. i. Tangential speeds are equal; ω1R1 = ω2R2 = ω2(2R1) therefore ω2 = ω1/2
ii. L = Iω = (16I1)(ω1/2) = 8I1ω1
iii. K = ½ I1ω12 + ½ I2ω22 = (5/2)I1ω12