A thin uniform circular disc of mass M and radius R is rotating in a horizontal plane about an axis passing through its centre and perpendicular to its plane with an angular velocity ω. Another disc of same dimensions but of mass $$14M$$ is placed gently on the first disc $$co-axially$$. The angular velocity of the system is

Question

A thin uniform circular disc of mass M and radius R is rotating in a horizontal plane about an axis passing through its centre and perpendicular to its plane with an angular velocity ω. Another disc of same dimensions but of mass $$14M$$ is placed gently on the first disc $$co-axially$$. The angular velocity of the system is

Infinity Learn · Accepted Answer

∴$$I1=MR22$$ and $$I2=MR22+12M4R2=58MR2By$$ conservation of angular momentum,Iω$$1=I2$$ω$$2$$⇒ω$$2=I1I2$$ω$$1=(1/2)MR2(5/8)MR2$$ω⇒ω$$2=45$$ω

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