Answer to Question #65497 in Mechanics | Relativity for Manoj

Question

A solid cylinder of mass 3.0 kg and radius 1.0 m is rotating about its axis with a speed of 40 rad s-1. Calculate the torque which must be applied to bring it to rest in 10s. What would be the power required?

Answer 1

Mass of the cylinder, m = 3.0 kg
Angular speed, ω = 40 rad s–1
Radius of the cylinder, r = 1.0 m
Time t = 10 s
The moment of inertia of the solid cylinder:
τ = Iα
I = mr2 / 2
α = ω / t
τ = m ω r2 / 2 t
τ = 3 kg x 40 rad s–1 x (1.0 m)2 / 2 x 10 s = 6 N m

Power given by
P = ω τ
P = 6 N m x 40 rad s–1 = 240 Wt