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A uniiform disc of radius r spins with a...

A uniiform disc of radius `r` spins with angular velocity `omega` and angular acceleration `alpha`. If the centre of mass of the disc has linear acceleration `a`, find the magnitude and direction of aceeleration of the point `1,2`, and `3`.

Text Solution

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The acceleration of point `1: veca_(1)=veca_(1,C)+veca_(C)`
But `veca_(1,C)=(veca_(1,C))_("tangential")+(veca_(1,C))_("radial")`

`implies veca_(1,C)=alpha Rhatj+omega^(2)Rhati` and `veca_(C)=ahati`
Hence `veca_(1)=(omega^(2)R+a)hati+alphaRhatj`
Similarly the acceleration of `2: veca_(2)=veca_(2), +veca_(C)`
Here `veca_(2,C)=(alphaRhati-omega^(2)Rhatj) ` and `veca_(C)=ahati`
Hence `veca_(2)=(a+alphaR)hati-omega^(2)Rhatj`
Also acceleration of 3, `veca_(3)=veca(3,c)=ahati`
Hence `veca_(3)=(a-omega^(2)R)hati-alphaRhatj`
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