Question

The rate of rotation of a solid disk with a radius of `4 m` and mass of `5 kg` constantly changes from `12 Hz` to `15 Hz`. If the change in rotational frequency occurs over `6 s`, what torque was applied to the disk?

Answer 1

The torque was `=125.7Nm`

Explanation:

The torque is the rate of change of angular momentum

`tau=(dL)/dt=(d(Iomega))/dt=I(domega)/dt`

where `I` is the moment of inertia

For a solid disc, `I=(mr^2)/2`

`I=5*4^2/2=40kgm^2`

The rate of change of angular velocity is

`(domega)/dt=(15-12)/6*2pi`

`=(pi) rads^(-2)`

So the torque is `tau=40*(pi) Nm=125.7Nm`