A body starts rotating from rest. Due to a torque of 10 N.m, it completes 300 rotations in one minute. Find the moment of inertia of the body.

Explanation

Data : ` omega_(0) = 0,t = 10N.m t =1 min = 60 s, ft = 300` rotations.
`theta = omegat = 2pift = 2oi xx 300 = 600 pi` rad
` theta = omega_(0)t+ 1/2 prop t^(2)`
` 600 pi = 0 + 1/2 ( 60 xx 60)`
` prop = ( 600 pi xx2)/( 60 xx 60) = pi/3 "rad/s"^(2)`
`t = I prop`
The moment of inertia of the body ` I = t/prop = 10/(pi//3) = 30/pi = 30 /3.142`
= `9.548 kg.m^(2)`