Physics torque problem (I have the answer but I do not understand how they got there, please help!)

Question

A 220 g , 25-cm-diameter plastic disk is spun on an axle through its center by an electric motor. What torque must the motor supply to take the disk from 0 to 1500 rpm in 4.5 s? (The answer is 6.0×10⁻² N⋅m) PLEASE HELP EXPLAIN THIS TO ME:)

Answer 1

Applied torque τ is related to angular acceleration α and moment of inertia I by the second law: τ = I α.

In this case, we have a (not hollow) disc of mass M and radius R spinning around an axes through its center, so I = 0.5MR^2.

The angular acceleration is such that it brings it from 0 to 1500rpm in 4.5 sec, so α = (1500 - 0)/4.5 = 34.906 rad/(s^2) [I converted "rpm" to "rad/s"]

Then, τ = I α = 0.5 * 0.220 * (0.25/2)^2 * 34.906 [Nm] = 6.0×10⁻² N⋅m