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A long horizontal rod has a bead which can slide along its length and initially placed at a distance 2L from one end A of the rod.The rod is set in angular motion about A with constant angular acceleration alpha.If the coefficient of friciton b/w the rod and the bead is mew,and gravity is neglected ,then the time after which the bead starts slipping is
t=underroot(mew/alpha)
See, the bead will start sliding when centripetalforce will be equal to limiting friction. Now there will be two forces on bead one tangential F(t)=ma=2lalpha.m (a=R.alpha).
And second F(c)=2ml(omega)''2 then using omega=alpha.t
Equate F(c)=mew.N where N is provided by F(t). S it becomes
2mL(alpha)''2(t)''2=2mewL(alpha)m
so for t>underroot (mew/alpha) bead starts sliding..
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