Question

Consult Multiple-Concept Example 10 to review an approach to problems such as this. A CD has a mass of 17 g and a radius of 6.0 cm. When inserted into a player, the CD starts from rest and accelerates to an angular velocity of 16 rad/s in 0.63 s. Assuming the CD is a uniform solid disk, determine the net torque acting on it.

Answer 1

Net torque acting on CD will be given by:

Torque = I*alpha

I = moment of inertia of CD = (1/2)*m*R^2

m = mass of CD = 17 gm = 0.017 kg

R = radius of CD = 6.0 cm = 0.06 m, So

alpha = angular acceleration

Using 1st rotational kinematic equation:

wf = wi + alpha*t

alpha = (wf - wi)/t

wi = 0 rad/sec & wf = 16 rad/sec, t = 0.63 sec, So

alpha = (16 - 0)/0.63 = 25.4 rad/sec^2

Using above values:

Torque = I*alpha = (1/2)*m*R^2*alpha

Torque = (1/2)*0.017*0.06^2*25.4

Torque = 7.8*10^-4 N.m

Please Upvote.