Question

An energy of $484J$ is spent in increasing the speed of a flywheel from $60rpm$ to $360rpm$. Calculate $M.I.$ of flywheel.

Answer 1

Given: An energy of 484J is spent in increasing the speed of a flywheel from 60 rpm to 360 rpm.

To find the M.I. of flywheel.

Solution:

Since 484J energy is supplied to it, then change in rotational kinetic energy is equal to the energy supplied to it.

INITIAL SPEED $V_1=60rpm=\frac{60\times 2\times 3.14rad}{60s}=6.28rad/s$

FINAL SPEED $V_2=360rpm=\frac{360\times 2\times 3.14rad}{60s}=37.68rad/s$

Rotational kinetic energy

$484=\frac{1}{2}I({\omega }_1^2-{\omega }_2^2)⟹484=\frac{1}{2}I\left(\right(37.68{)}^2-\left(6.28{)}^2\right)⟹484=690.17I⟹I=0.7kg{m}^2$

is the M.I. of flywheel.