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Q.A statioonary horizontal uniform circular disc of mass m and radius r can freely rotate about its axis.Now,it starts experiencing a torque τ(tau)=aO(theta)+b,where O is the angular displacement of disc and a ,b are positive constants.Find the angular velocity of disc as a function of O(theta).
T(tau)=aO + b (O= angular displacement)
T=I @
@ = angular accleration
@=dw/dt = (dw/do) (do/dt) ( on multplying and dividing by Do)
@do = wdw (do/dt =w)
(aO + b)do =wdw
(aO2/2 +bO) =w2 /2 or
w = (aO2 +2bO)1/2
this is the rquired solution...
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