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Energy of 1000 J is spent in increasing ...

Energy of 1000 J is spent in increasing the speed of a flywheel from 30 rpm to 720ppm, find the moment of inertia of the wheel

Text Solution

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`omega_(1)=30 rpm= 2pi xx(30)/(60)"rad" s^(-1)= pi "rad" s^(-1)`
`omega=720 rpm= 2pi xx(720)/(60) "rad" s^(-1)=24 pi "rad"`
Change in kinetic energy
`DeltaKE=(1)/(2)(omega_(2)^(2)-omega_(1)^(2))`
`I=(2xxDeltaKE)/((omega_(1)^(2)-omega_(1)^(2)))=(2xx1000)/((24pi)^(2)-(pi)^(2))`
`I=(2000)/(25 pixx23 pi)` Remember : `a^(2)-b^(2)=(a+b)(a-b)`
`I~~0.35 kg m^(2) and pi^(2)=10`
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