Angular Momentum and Angular Impulse AP Physics C Mechanics FRQ – Exam Style Questions etc.
Angular Momentum and Angular Impulse AP Physics C Mechanics FRQ
Unit 6: Energy and Momentum of Rotating Systems
Weightage : 10-15%
Question
A system consists of two small disks, of masses m and 2m, attached to a rod of negligible mass of length 3l as shown above. The rod is free to turn about a vertical axis through point P. The two disks rest on a rough horizontal surface; the coefficient of friction between the disks and the surface is µ. At time t = 0, the rod has an initial counterclockwise angular velocity ωo about P. The system is gradually brought to rest by friction. Develop expressions for the following quantities in terms of µ m, l, g, and ω0
a. The initial angular momentum of the system about the axis through P
b. The frictional torque acting on the system about the axis through P
c. The time T at which the system will come to rest.
Answer/Explanation
Ans:
a. L = Iω where I = Σmr2 = (2m)l2 + m(2l)2 = 6ml2
L = 6ml2ω
b. Ff = µmg
Στ = –(µ(2m)gl + µmg(2l)) = –4µmgl
c. α = τ/I = –4µmgl/6ml2 = –2µg/3l
ω = ω0 + αt; setting ω = 0 and solving for T gives T = 3ω0l/2µg