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The angular velocity of a gar is control...

The angular velocity of a gar is controlled according to `omega=12-3t^(2)` where `omega` in radian per second, is positive in the clockwise sense and `t` is the time in seconds. Find the net angular displacement `triangletheta` from the time `t=0` to `t=3`s. Also, find the number of revolutions `N` through which the gear turns during the 3s.

Text Solution

Verified by Experts

`theta=int_(0)^(3)omegadt=int_(0)^(3)(12-3t^(2))dt`
`=36-27=9rad`
`N=(theta)/(2pi)=(9)/(2xx3.14)=1.43`
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