Answer to Question #274091 in Physics for thea

Question

A certain flywheel is acted upon by a constant torque of 45 N-m. Find the time it takes to go from rest to an angular velocity of 812 rev/min if the moment of inertia is 5 kg-m2?

Answer 1

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

$$\tau=I\alpha,$$ $$\alpha=\dfrac{\tau}{I}=\dfrac{45\ N\times m}{5\ kg\times m^2}=9\ \dfrac{rad}{s^2}.$$

Finally, we can find the time the flywheel takes to go from rest to an angular velocity of 812 rev/min:

$$\omega=\omega_0+\alpha t,$$ $$t=\dfrac{\omega-\omega_0}{\alpha},$$ $$t=\dfrac{812\ \dfrac{rev}{min}\times\dfrac{1\ min}{60\ s}\times\dfrac{2\pi\ rad}{1\ rev}-0}{9\ \dfrac{rad}{s^2}}=9.4\ s.$$