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A thin uniform circular disc of mass M a...

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 the plane with angular velocity `omega`. Another disc of same mass but half the radius is gently placed over it coaxially. The angular speed ofthe composite disc will be:

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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 omega . Another disc of the same dimension but of mass M/4 is placed gently on the first disc coaxially. Show that the angular momentum of the system is (4)/(5)omega .