Question

A turntable must spin at 33.3 rev/min (3.49 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 1.70 revolutions, starting from rest? The turntable is a uniform disk of diameter 30.5 cm and mass 0.220 kg.

Answer 1

To calculate the torque required for the turntable to reach its final angular speed, you can use the torque equation. The moment of inertia for a uniform disk rotating about its center is (1/2) * Mass * Radius^2. Use the angular acceleration formula to find the required torque.

Step-by-step explanation:

To calculate the torque required for the turntable to reach its final angular speed, we can use the torque equation:

Torque = Moment of Inertia * Angular Acceleration

The moment of inertia for a uniform disk rotating about its center is given by:

Moment of Inertia = (1/2) * Mass * Radius^2

Using the given values for mass and diameter, we can calculate the moment of inertia. Since the turntable starts from rest, the initial angular velocity is 0 rad/s. We can use the angular acceleration formula to find the required torque.