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Answer :
The new angular velocity is 27.7 rpm
From the question, we have
ω = 22 rpm = angular velocity with all children on the edge,
ω' = angular velocity after m2 moved.
From conservation of angular momentum, we have
Mr²ω'/2 + m1r²ω' + m3r²ω' = Mr²ω/2 + m1r²ω + m2r²ω + m3r²ω
ω' = ω(M/2 + m1 + m2 + m3)/(M/2 + m1 + m3)
ω' = 22×(115/2 + 32 + 34 + 40)/(115/2 + 32 + 40)
= 27.7 rpm
The new angular velocity is 27.7 rpm
Complete question:
three children are riding on the edge of a merry-go-round that is 115 kg, has a 1.7-m radius, and is spinning at 24 rpm. the children have masses of 32, 34, and 40 kg. (a) if the children with masses of 34 and 40 kg move to the center of the merry-go-round, what is the new angular velocity in rpm?
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