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 `1 Hz` to `5 Hz` in `3 s`, what torque was applied to the object?

Answer 1

The torque is `=268.1Nm`

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 the object, `I=mr^2`

So, `I=2*(4)^2=32kgm^2`

The rate of change of angular velocity is

`(Deltaomega)/(Deltat)=((5-1)*2pi)/(3)=8/3pirads^-2`

So,

The torque is

`tau=32*8/3pi=268.1Nm`