Question

The angular speed of a flywheel changes from 10 rad/s to 20 rad/s in 5 seconds when a torque of 20 N.m is applied to it. Calculate the MI of the flywheel.​

Answer 1

$\large{\bf{\gray{\underline{\underline{\orange{Given:}}}}}}$

Initial angular speed = 10rad/s

Final angular speed = 20rad/s

Applied torque = 20Nm

$\large{\bf{\gray{\underline{\underline{\green{To\:Find:}}}}}}$

We have to find MI (Moment of Inertia) of the flywheel.

$\large{\bf{\gray{\underline{\underline{\pink{Solution:}}}}}}$

➠ Torque is defined as the rate of change of angular momentum.

$\dag\:\underline{\boxed{\bf{\red{\tau=\dfrac{dL}{dt}}}}}$

➠ Angular momentum is defined as the product of angular speed and MI.

$\dag\:\underline{\boxed{\bf{\blue{\tau=\dfrac{I(\omega_f-\omega_i)}{dt}}}}}$

Let's calculate :D

$:\implies\tt\:\tau=\dfrac{I(\omega_f-\omega_i)}{dt}$

$:\implies\tt\:20=\dfrac{I(20-10)}{5}$

$:\implies\tt\:100=10I$

$:\implies\boxed{\bf{\purple{I=10\:kgm^2}}}$