Question

An energy of `484 J` is spent in increasing the speed of a flywheel from 60 rpm to 360 rpm. Calculate moment of inertia of flywheel.

Answer 1

Energy spent, `W=484 J`
Initial speed, `omega_(1)=60 "rpm" = (60)/(60)xx2pi=2pi "rad s"^(-1)`
Final speed, `omega_(2)=360 "rpm" = (360)/(60)xx2pi=12 pi "rad s"^(-1)`
Moment of inertia, `I = ?`
Energy spend, `W=E_(2)-E_(1)=(1)/(2) I omega_(2)^(2) - (1)/(2) I omega_(1)^(2)`
`= (1)/(2) I[(12 pi)^(2) - (2 pi)^(2)]=70 I pi^(2)`
`rArr I=(484)/(70xxpi^(2))=0.7 "kg-m"^(2)`.