Question

a torque of 500 N.m is applied to a fly wheel rotating at 200 rad/s. After 40 s its speed has doubled. What is the flywheel moment of inertia?

Answer 1

A torque of $500\,\mathrm{Nm}$ is applied to a fly wheel rotating at 200 rad/s. After 40 s its speed has doubled. What is the flywheel moment of inertia?

Newton's second law of motion adapted to describe the relation between torque and angular acceleration:

$$\tau = I \alpha$$

where $\tau$ – torque, $I$ – moment of inertia, $\alpha$ – angular acceleration.

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

The angular acceleration can be defined as:

$$\alpha = \frac{\Delta \omega}{\Delta t}$$

Therefore:

$$\frac{\Delta \omega}{\Delta t} = \frac{\tau}{I}$$ $$I = \frac{\tau}{\frac{\Delta \omega}{\Delta t}} = \frac{\tau \Delta t}{\Delta \omega} = \frac{500\,N * m * 40\,s}{200\,\frac{\mathrm{rad}}{\mathrm{s}}} = 100\,\mathrm{kg} * m^2$$

Answer: $100\,\mathrm{kg} * m^2$