When 100 J of work is done on a fly wheel, its angular velocity is increased from 60 rpm to 180 rpm. What is the moment of inertia of the wheel?

Explanation

K.E=100 J,`n_(1)`=60 rpm =1 rps,`n_(2)`=180 rpm =3rps
Increase in kinetic energy `E=(1)/(2)I(omega_(2)^(2)-omega_(1)^(2))=(1)/(2)I(4pi^(2)n_(2)^(2)-4pi^(2)n_(1)^(2))`
`100=(1)/(2)I(4pi^(2).9-4 pi^(2)1^(2))=2pi^(2)I(9-1)=16pi^(2).I`
`therefore` momeny of inertia of the wheel I =`(100)/(16 mpi^(2))=0.633 kg m^(2)`