A solid cylinder of mass m = 3 kg and radius r = 12 cm is initially rotating about its central axis with angular frequency = 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 torque is:τ = Fr = (0.5 N)(0.12 m) = 0.06 NmThe angular acceleration is:α = τ/I = (0.06 Nm)/(0.45 kg m^2/s) = 0.133 rad/s^2The final angular velocity is:ωf = ωi + αtwhere t is the time it takes for the cylinder to stop rotating. We can find t by using the equation:ωf = ωi + αt0 = 25 rad/s + (-0.133 rad/s^2)tt = 187.9 sThe number of revolutions the cylinder makes is:n = ωft/2π = (0 rad/s)(187.9 s)/(2π rad) = 0.018 revTherefore, the correct answer is A.

A Solid Cylinder of Mass M = 3 Kg and Radius