Answer to Question #164635 in Physics for Treasure Enyinnaya

Question

A retarding torque of 600 N-m is applied to a flywheel rotating at 240 r.p.m Find the moment of inertia of the flywheel, if it conies to rest in 100 seconds.

(Ans. 2390 kg-nr)

Answer 1

Let's first find the angular acceleration of the flywheel:

$$\alpha=\dfrac{\omega_f-\omega_i}{t},$$ $$\alpha=\dfrac{0-240\ \dfrac{rev}{min}\cdot\dfrac{1\ min}{60\ s}\cdot2\pi\ rad}{100\ s}=-0.251\ \dfrac{rad}{s^2}.$$

The sign minus means that the flywheel decelerates.

Finally, we can find the moment of inertia of the flywheel from the formula:

$$\tau=I\alpha,$$ $$I=\dfrac{\tau}{\alpha}=\dfrac{-600\ N\cdot m}{-0.251\ \dfrac{rad}{s^2}}=2390\ kg\cdot m^2.$$