Question

A flywheel in the form of a disk with mass m = 50 kg and radius R = 20 cm, rotates with frequency f = 480 rpm. Under the action of a braking moment the flywheel stops performing N = 200 rotations from the start of braking until complete stop. To find this moment.

Answer 1

Find the angular deceleration:

$$\alpha=\frac{\Delta \omega^2}{2\Delta \phi}=\frac{(2\pi f)^2}{4\pi N}=\frac{\pi f^2}{N}.$$

The moment:

$$\tau=I\alpha=\frac12mr^2\alpha=\frac{\pi mr^2f^2}{2N},\\\space\\ \tau=0.251\text{ N-m}$$