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A pulley os radius 2m is rotated about i...

A pulley os radius 2m is rotated about its axis by a force `F= (20 t- 5t^2)` newton (where t is measured in seconds) applied tangentially. If the moment of inertia of the pulley about its axis of rotation is `10kg m^2` the number of rotaitons made by the pulley before its direction of motion is reversed, is:

Text Solution

Verified by Experts

Given force, `F=20 t-5t^(2)`
`alpha=(FR)/I=((20t-5t^(2))2)/10=4t-t^(2)`
`rArr(domega)/(dt)=4t-t^(2)rArrint_(0)^(omega)domega=int_(0)^(t)(4t-t^(2))dt`
`rArromega =0, i.e., t=0` to `6s` Now.
`d theta=omegadtrArrint_(0)^(theta)d theta=int_(0)^(6)(2t^(2)-(t^(3))/3) dt`
`rArrtheta=[(2t^(3))/3-(t^(4))/12]_(0)^(6)rArrtheta=144-108=36 rad `
`:.` Number of rotations, `n =(theta)/(2pi)=36/(2pi)lt6`
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