A solid cylinder of mass m = 3 kg and radius r = 12 cm is initially rotating about its central axis with angular frequency $\omega$ = 25 radians/s.How many revolutions does it make after a retarding force of 0.5 N is applied to the outer surface?
A)0.018 rev
B)0.11 rev
C)0.036 rev
D)0.0090 rev
E)0.072 rev

Question

Quizplus · Accepted Answer

Explanation:The initial angular momentum of the cylinder is:L = Iω = (1/2)mr^2ω = (1/2)(3 kg)(0.12 m)^2(25 rad/s) = 0.45 kg m^2/sThe retarding force will cause the angular momentum to decrease at a rate of:τ = -F = -0.5 Ndω/dt = -τ/I = -(-0.5 N)/(0.45 kg m^2/s) = 1.11 rad/s^2The time it takes for the cylinder to stop rotating is:ω = ω0 + αt0 = 25 rad/s + (-1.11 rad/s^2)tt = 22.5 sThe number of revolutions the cylinder makes during this time is:N = ωt/2π = (0 rad/s)(22.5 s)/2π = 0.018 rev

A Solid Cylinder of Mass M = 3 Kg and Radius