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.
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:.
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.