Three children are riding on the edge of a merry-go-round that is 105 kg, has a

Question

Three children are riding on the edge of a merry-go-round that is 105 kg, has a 1.40-m radius, and is spinning at 22.0 rpm. The children have masses of 22.0, 28.0, and 33.0 kg. If the child who has a mass of 28.0 kg moves to the center of the merry-go-round, what is the new angular velocity in rpm? Ignore friction, and assume that the merry-go-round can be treated as a solid disk and the children as points.

o 10/27/2017 06:00 PM O 93.1/ 10010/24/2017 04:03 PM Gradebook Print Calculator Periodic Table Question 17 of 17 Map Openstax College Physics presented by Sapling Leaming Three children are riding on the edge of a merry-go-round that is 105 kg, has a 1.40-m radius, and is spinning at 22.0 rpnm 28.0 kg moves to the center of the mer and assume that the merry-go-round children e masses of 22.0, 28.0, and 33.0 kg. If the child who has a mass of und, what is the new angular velocity in rpm? Ignore friction, can be treated as a solid disk and the children as points Number 66.4 rpm There is a hint available! View the hint by clicking on the bottom divider bar. Click on the divider bar again to hide the hint. Close Previous Check Answer NexExit Hint

Explanation / Answer

using law of conservation of angular momentum

initial angular momentum = final angular momentum

I1*w1 = I2*w2

I1 = (0.5*M*R^2)+(m1*R^2)+(m2*R^2)+(m3*R^2) = (0.5*105*1.4^2)+((22+28+33)*1.4^2) = 265.58 Kg-m^2

w1 = 22 rpm

I2 = 265.58-(m2*R^2) = 265.58-(28*1.4^2) = 210.7 kg-m^2

then

I1*w1 = I2*w2

265.58*22 = 210.7*w2

w2 = 27.73 rpm

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