Two men of mass 100 kg and mass 80 kg sit at the edge of a merry-go-round with a

Question

Two men of mass 100 kg and mass 80 kg sit at the edge of a merry-go-round with a 2 meter radius. The merry-go-round is initially rotating with an angular speed of 10 rpm. If the 80-kg man walks inward on the merry-go-round and stops a distance of 1 meter from the center O about which the ride is spinning, estimate the new angular speed of the system. You may assume that the merry-go-round rotates with negligible friction and has a much smaller mass than the men. a) omega = 12.9 rpm b) omega = 13.5 rpm c) omega = 14.3 rpm d) omega = 15 rpm

Explanation / Answer

Using Conservation of Angular Momentum,
Initial Angular Momentum = Final Angular Momentum
Ii * i = If * f

i = 10 rpm
Ii = m1*r^2 + m2*r^2
r = 2.0 m

If = m1*(r/2)^2 + m2*r^2

Substituing Values,
(80 * 2^2 + 100 * 2^2 ) * 10 = (80 * 1^2 + 100*2^2) * f
f = 15 rpm
Correct option :- (d)

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