A turntable must spin at 33.7 rpm (3.53 rad/s) to play an old-fashioned vinyl record. How much torque must the motor deliver if the turntable is to reach its final angular speed in 1.5 revolutions, starting from rest? The turntable is a uniform disk of diameter 30.5 cm and mass 0.27 kg.

Answer 1

Kinematic of rotational motion gives
2•π•N=ε•t^2/2
ω= ε•t.
Therefore,
ε = ω^2/4•N.
The moment of inertia (disc)
I = m•R^2/2.
M =I• ε