Question

A flywheel with moment of inertia $0.4kg{m}^2$ is free rotate in vertical plane about horizontal axis passing through its centre without friction. An external torque $10Nm$ is acting on the fly wheel which is initially stationary. The angular velocity of flywheel when it completes $100/\pi$ rotations is:

• A. $40rad/s^{-1}$
• B. $50rad/s^{-1}$
• C. $80rad/s^{-1}$
• D. $100rad/s^{-1}$

Answer 1

The correct option is D $100rad/s^{-1}$

Using the equation ,
$T=I\times a^{\prime }$
$10=0.4\times a^{\prime }$
$a^{\prime }=25rad/s^2$
now using equation of motion as given below,
$w_2^2=w^2+2a^{\prime }\theta$
$w_2^2=2\times 25\times 200$
$w_2=100rad/s$