Q. 25

A flywheel of moment of inertia 5.0 kg-m2 is rotated at a speed of 60 rad/s. Because of the friction at the axle, it comes to rest in 5.0 minutes. Find (a) the average torque of the friction, (b) the total work done by the friction and (c) the angular momentum of the wheel 1 minute before it stops rotating.

Answer :

The average torque is


The work done by the flywheel is


The angular momentum before stoppage of flywheel in 1 min is


Given


The moment of inertia of the flywheel is given as , the angular speed of the flywheel is given as 60 rad/sec and the time till it comes to rest is 5 minutes.


Formula Used


To find the average torque we use the formula as



For the calculation of work done from the torque of the flywheel



The angular momentum of the wheel is calculated as



where


L is the angular momentum, I is the moment of Inertia, ω is the angular velocity, W is the work done by the angular velocity, α is the angular acceleration and denotes the torque generated.


Explanation


First let us calculate the angular acceleration that will be



a) Now let us calculate the average torque of the flywheel which will be



The work done by the torque of the flywheel is




b) The angular momentum of the wheel in a time span of (5-1=4) minutes is


First let us find the angular velocity of the flywheel which is




Now placing the value of angular velocity in the formula of angular momentum we get the answer as




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