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A string is wrapped over the edge a unif...

A string is wrapped over the edge a uniform disc and the free end is fixed with the ceiling. The disc moves down, unwinding the string. Find the downward acceleration of the disc.

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The force translates the C.M. of the disc with an acceleration .a. given as
`F = ma" "rArr" "a = (F)/(m)`
The force F develops a torque `tau` about O, consequently the disc rotates with an angular acceleration `alpha` about an axis passing through O, given as `tau = I_(0) alpha`
`because " "tau = FR " "& I_(0) = (1)/(2)mR^(2)`
`rArr" "alpha = (tau)/(I_(0)) = (FR)/((1//2)mR^(2))=(2F)/(mR)`
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