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Question

A thin circular ring of mass M and radius R is rotating about its axis with an angular speed ω0. Two particles each of mass m are now attached at diametrically opposite points. The new angular speed of the ring is ω0MM+xm. Find x

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Solution

Since , there is no external force applied during addition of mass, angular momentum is conserved.
Iintialω0=Ifinalωfinal
Iintial=MR2
Ifinal=MR2+mR2+mR2
by substituting above in equation,
MR2ω0=(MR2+mR2+mR2)ωfinal
ωfinal=Mω0M+2m

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