Question

An object with a mass of `2 kg` is traveling in a circular path of a radius of `4 m`. If the object's angular velocity changes from `2 Hz` to `7 Hz` in `2 s`, what torque was applied to the object?

Answer 1

The torque is `=502.7m`

Explanation:

The torque is the rate of change of angular momentum.

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

The moment of inertia is `I=mr^2`

`I=2*4^2=32kgm^2`

The rate of change of angular velocity is

`(domega)/dt=(7-2)/2*2pi`

`=5pi rads^(-2)`

So the torque is `tau=32*5pi Nm=502.7Nm`