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When 100 J of work is done on a fly whee...

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?

Text Solution

Verified by Experts

Here, Initial frequency
`n_(1)=(60)/(60)=1Hz`
Initial angular velocity
`omega_(1)=2pin_(1)=2pi" rad/sec"`
Final frequency `n_(2)=(180)/(60)=3Hz`
Final angular velocity
`omega_(2)=2pin_(2)=2pixx3=6pi" rad/sec"`
Work done = 100 j
from work - energy theorem,
Workdone = change in K.E.
`W=(1)/(2)Iomega_(2)^(2)-(1)/(2)Iomega_(1)^(2)`
`100=(1)/(2)I[(6pi)^(2)-(2pi)^(2)]`
`100=(1)/(2)I(32pi)^(2)`
`I=(200)/(32pi^(2))=0.634kg-m^(2)`
`therefore I=0.634kg-m^(2)`.
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