Question

A torque t acts on a body of moment of inertia I rotating with angular speed omega it will stop just after time

Answer 1

Answer:

The time taken to stop is $\frac{\omega I}{\tau}$

Explanation:

Given

Moment of Inertia $=I$

Angular velocity $=\omega$

Torque $=\tau$

The angular acceleration of the body

$\alpha=\frac{\tau}{I}$

Since the torque acts to stop the body

Therefore the angular acceleration will be negative

Let the body stops in time t

Then using the second equation of motion for rotation

$\omega'=\omega+\alpha t$

$0=\omega-\alpha t$

$\implies \frac{\tau}{I}\times t=\omega$

$\implies t=\frac{\omega I}{\tau}$

Hope this helps.