33. A uniform circuiar disc with its planehorizontal is rotating about

1.	33. A uniform circuiar disc with its planehorizontal is rotating about a vertical axispassing through its centre at a speed of180 r.p.m. A small piece of wax of mass 1.9g falls verticaliy on the disc and sticks to itat a distance of 25 cm from the axis.If thespeed of rotation is now reduced by 60r.p.m. calenlate moment of inertia of thedisc. [Feb. 2015]s
Answer» During the process of mass m being added and the disc rotating making less revolutions the thing which remains constant is Angular momentum.So we need to conserve angular momentum. FormomentofinertiaIandangularvelocityωandangularfrequencyvIω=Iν=constantorI1ω1=I2ω2orLetmomentofinertiaofdiscbeI,wehavebeengiventhefrequencyas90rev.persecWhenmassmisbeingaddedweuseparallelaxistheorumsofinalmomentofinertiawith60rev.persecbecomes(I+mr^2).SoI×90=(I+mr^2)×603I=2I+2mr^2I=2mr^2

33. A uniform circuiar disc with its planehorizontal is rotating about a vertical axispassing through its centre at a speed of180 r.p.m. A small piece of wax of mass 1.9g falls verticaliy on the disc and sticks to itat a distance of 25 cm from the axis.If thespeed of rotation is now reduced by 60r.p.m. calenlate moment of inertia of thedisc. [Feb. 2015]s

Answer»

During the process of mass m being added and the disc rotating making less revolutions the thing which remains constant is Angular momentum.So we need to conserve angular momentum.

FormomentofinertiaIandangularvelocityωandangularfrequencyvIω=Iν=constantorI1ω1=I2ω2orLetmomentofinertiaofdiscbeI,wehavebeengiventhefrequencyas90rev.persecWhenmassmisbeingaddedweuseparallelaxistheorumsofinalmomentofinertiawith60rev.persecbecomes(I+mr^2).SoI×90=(I+mr^2)×603I=2I+2mr^2I=2mr^2

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