Question

A 240 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 2000 rpm in 4.3 s ?
Express your answer in newton-meters.

t=

Answer 1

Given, the disc rotates from 0 to 2000rpm in t = 4.3s. So the initial angular speed of the disk is = 0rad/s. Also the final frequency of rotation of disk is 2000rpm. Therefore,

So the final angular speed of the disc is,

The angular acceleration of the disc is given by,

So the angular acceleration of the disc is 48.70rad/s^2.

Given the mass of the disc M = 240g = 0.240 kg and the diameter of the disk d = 25cm. So the radius of the disk is R = 12.5cm = 0.125m. The moment of inertia of the disc about an axis passing through the centre is given by,

The torque supplied by the motor is given by,

So the torque supplied by the motor is 0.091Nm.