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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

Given: Initial angular velocity `omega_(0)=20 pi"rad"//s`
Final angular velocity `omega=40pi "rad"//s`
Time `t=10s`
Solution: Angular acceleration `alpha=(omega-omega_(0))/(t)=(40pi-20pi)/(10)`
`alpha=2pi "rad"//s^(2)`
According to equation of motion for rotational motion
`theta= omega_(0)t+(1)/(2)alpha t^(2)=20 pixx10+(1)/(2)2pixx100=300 pi` rad `n=(300pi)/(2pi)=150` rotations.
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