Question

An object with a mass of `8 kg` is traveling in a circular path of a radius of `12 m`. If the object's angular velocity changes from `5 Hz` to `7 Hz` in `6 s`, what torque was applied to the object?

Answer 1

The torque is `=2412.7Nm`

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

The mass of the object is `m=8kg`

The radius of the path is `r=12m`

For the object, `I=mr^2`

So, `I=8*(12)^2=1152kgm^2`

And the rate of change of angular velocity is

`(d omega)/dt=(Deltaomega)/t=(2pif_1-2pif_2)/t`

`=(14pi-10pi)/6=(2/3pi)rads^-2`

So,

The torque is

`tau=1152*2/3pi=2412.7Nm`