A child ( m c = 44 kg) is playing on a merry-go-round ( m m = 235 kg, R = 3.0 m)
ID: 2299187 • Letter: A
Question
A child (mc = 44 kg) is playing on a merry-go-round (mm = 235 kg, R = 3.0 m) that is initially at rest. The child then jumps off in a direction tangent to the edge of the merry-go-round as shown in the figure below. The child has a speed of 5.0 m/s just before she lands on the ground.
What is the initial angular momentum of your system?
Make a sketch showing your system just before and just after the child jumps off the merry-go-round.
If the final angular velocity of the merry-go-round is ?f, what is the magnitude of the final angular momentum of the merry-go-round? Express your answer in terms of ?f. (Use the following as necessary: mm, ?f and R. Do not substitute numerical values; use variables only.)
Lf,m =
What is the magnitude of the final angular momentum of the child? Express your answer in terms of
?f. (Use the following as necessary: mc, ?f and R. Do not substitute numerical values; use variables only.)
Lf,c =
What is the magnitude of the final angular velocity of the merry-go-round?
_____rad/s
Explanation / Answer
1) Li = 0
2) for merry go round Lf = If*?f
Lf = (1/2)*Mm*R^2*?f
3) Lf of child = m*v*R
(1/2)*Mm*R^2*?f + m*v*R = 0
?f = -2*Mc*v/(Mm*R)
0.5*235*3*?f = 44*5
?f = 0.624 rad/s
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