Problem

Unless otherwise stated, in the following problems we assume that the gravitational force is constant with g = 9.81 m/sec2 in the MKS system and g = 32 ft/sec2 in the U.S. Customary System.

In Problem 16, let I = 50 kg-m2 and the retarding torque be N-m. If the motor is turned off with the angular velocity at 225 rad/sec, determine how long it will take for the flywheel to come to rest.

Step-1:

In this problem we need to find the time when the flywheel to come to rest.

Let us consider, the angular velocity is .

Torque from the motor is T.

The moment of inertia of flywheel is .

Initial angular velocity of the flywheel is .

Retarding torque due to friction is proportional to the angular velocity .

That is, , where k is the proportional constant.

By newton’s second law for rotation of motion we have:.

That is,

Therefore,

Step-2:

Given:

Proportionality constant k = 5.

Angular velocity and

We know that , at the initial stage motor is turned off.So,T=0.

Now the above equation becomes:

.

Now it is in variable separable form.

Integrating on both sides we get.