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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).

509 Points
10 years ago

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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