Answer to Question #114144 in Mechanics | Relativity for Feker

Question

A fly wheel has a moment of inertia of 3.8kgm^2.what constant is required to increase its frequency from 2rev/sec to 5rev/sec in 6 revolutions?

Answer 1

6 revolutions correspond to angular displacement of $\phi=6\cdot2\pi=12\pi$.

To increase the angular velocity, there must be angular acceleration:

$$\alpha=\frac{\omega_2^2-\omega_1^2}{2\phi}=2\pi^2\cdot\frac{n_2^2-n_1^2}{\phi}=11\text{ rad/s}^2.$$

The torque required to provide such acceleration is

$$\tau=I\alpha=41.8\text{ N}\cdot\text{m}.$$