A 36.5 kg child stands at the center of a 125 kg playground merry-go-round which rotates at 3.10 rad/s. If the child moves to the edge of the merry-go-round, what is the new angular velocity of the system? Model the merry-go-round as a solid disk. |
Mass of child = m = 36.5 kg
Mass of merry-go-round = M = 125 kg
Radius of the merry-go-round = R
Initial angular velocity of the merry-go-round =
1 = 3.1 rad/s
Final angular velocity of the merry-go-round =
2
Moment of inertia of merry-go-round = I = MR2/2
Speed of child at the edge of the merry-go-round = V =
2R
By angular momentum conservation,
I1
= I
2
+ mVR
(MR2/2)1
= (MR2/2)
2
+ m(
2R)R
M1/2
= M
2/2
+ m
2
(125)(3.1)/2 =
2(125/2 + 36.5)
2
= 1.957 rad/s
The new angular velocity of the system = 1.957 rad/s
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