Question

When the play button is pressed, a CD accelerates uniformly from rest to 420 rev/min in 5.0 revolutions.
Part A
If the CD has a radius of 6.5 cm and a mass of 20 g , what is the torque exerted on it?
Express your answer using two significant figures. N.m

Answer 1

Time required to get up to speed:
theta = (1/2)(w0 + w)*t
5 rev = (1/2)(0 rev/s + 420/60 rev/s)*t
t = 1/7 s

Angular speed that the CD gets up to:
420/60 rev/sec *2 π rad/rev
= 14 π rad/s

Angular acceleration of CD:
alpha = (14 π rad/s - 0 rad/s)/(1/7)s
alpha = 98 π rad/s^2

Moment of inertia of CD:
I = mk^2
I = (0.020 kg)(0.065 m)^2
I = 8.45 * 10^-5 kg*m^2

Torque exerted on CD:
Ta = I*alpha
Ta = (______)(______)
Ta = ______ N*m

Answer 2

The previous response is correct except that Inertia for a disk or solid cylinder = (1/2)(M)(R^2)