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A fly wheel rotates with a uniform angul...

A fly wheel rotates with a uniform angular acceleration. If its angular velocity increases form `20 pi` rad/s to `40 pi` rad/s in 10 seconds. Find the number of rotations in that period.

Text Solution

Verified by Experts

`omega_(1)=20 pi` rad/s
`omega_(2)=40pi` rad/s
`t=10s`
`omega_(2)=omega_(1)+alphat`
`alpha=(omega_(2)-omega_(1))/t=(40pi-20pi)/10`
`=2pi` rad/s
`:.` Angle of rotation is
`theta=omega_(1)t+1/2 alphat^(2)`
`theta=200 pi +1/2 xx2pixx10^(2)`
`=200pi+100pi`
`theta=300pi`
`:.` Number of rotations
`n=(theta)/(2pi)=(300pi)/(2pi)`
`=150` rotations
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