8. An unpowered flywheel is slowed by a constant frictional torque. At time t = 0 it has an angular velocity of 200 rad/s. Ten seconds later its velocity has decreased by 15%. What is its angular velocity at a) time t = 50 s and b) t = 100 s?

a) , b)

Explanation:

The magnitude of torque is a form of moment, that is, a product of force and lever arm (distance), and force is the product of mass and acceleration for rotating systems with constant mass. That is:

Where is the angular acceleration, which is constant as torque is constant. Angular deceleration experimented by the unpowered flywheel is:

Now, angular velocities of the unpowered flywheel at 50 seconds and 100 seconds are, respectively:

a) t = 50 s.

b) t = 100 s.

Given that friction is of reactive nature. Frictional torque works on the unpowered flywheel until angular velocity is reduced to zero, whose instant is:

Since , then the angular velocity is equal to zero. Therefore: