Question

An object with a mass of `3 kg` is traveling in a circular path of a radius of `7 m`. If the object's angular velocity changes from `3 Hz` to `7 Hz` in `3 s`, what torque was applied to the object?

Answer 1

We will use cassical mechanics (rotation) equations to solve this problem.

Explanation:

With frequency of `3Hz` the velocity is `ω_1=2pif_1=6pi(rads)/s`

With frequency of `7Hz` the velocity is `ω_2=2pif_2=14pi(rads)/s`

The angular acceleration is then

`α=(Δω)/(Δt)=(14pi-6pi)/3=(8pi)/3(rads)/s^2`

and the torque is :

`Τ=Iα=mr^2α=3*49*(8pi)/3=392piNm`