A turntable must spin at 33.4 rpm (3.50 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 1.0 revolutions, starting from rest? the turntable is a uniform disk of diameter 30.5 cm and mass 0.21 kg.

In order to compute the torque required, we may apply Newton's second law for circular motion:

Torque = moment of inertia * angular acceleration

For this, we require the angular acceleration, α. We may calculate this using:

α = Δω/Δt

The time taken to achieve rotational speed may be calculated using:

time = 1 revolution * 2π radians per revolution / 3.5 radians per second

time = 1.80 seconds

α = (3.5 - 0) / 1.8

α = 1.94 rad/s²

The moment of inertia of a thin disc is given by:

I = MR²/2

I = (0.21*0.1525²) / 2

I = 0.002

τ = 1.94 * 0.002

τ = 0.004

The torque is 0.004