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 25 rad/s in 0.59 s. Assuming the CD is a uniform solid disk, determine the net torque acting on it.

Answer 1

τ: torque
I: momento of inertia
α: angular acceleration

You know that τ = I α

Moment of inertia for a solid disk is I = m*r^2/2
In SI units you have m = 0.017kg and r =0.06m
So I = (0.017*0.06² )/2 = 3.06*10^-5 kg m^{​​​​​​2}

The disk goes from 0 to 25 rads/s in 0.59s so its angular acceleration (supposed constant)
is α = 25/0.59 = 42.37 rad/s^2

$\tau$ = 3.06*10^-5 * 42.37 = 12.96*10^-4 Nm

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Forming the product of I and α the torque is 7.96*10^(-4) Nm