Two children, Angelica (mass 35 kg ) and Boris (mass 50 kg ), are playing on a merry-go-round (which you can assume is a solid disk with mass 200 kg and radius 1.5m). Assume that any friction on the axle of the merry-go-round is negligible.
A.) Angelica starts spinning the merry-go-round, giving it an angular velocity of 8 rad/s , then she stops pushing it. Boris runs with a speed of 9 m/s directly toward the center of the merry-go-round. He jumps and lands on the edge of the merry-go-round. What is the angular speed of the merry-go-round once Boris lands on it?
B.) After landing, Boris walks to the center of the merry-go-round. What is the angular speed of the merry-go-round when he gets to the center?
C.) While Boris is in the center of the merry-go-round, Angelica runs up with a speed of 6 m/s tangentially in the same direction the merry-go-round is spinning, jumping onto the edge of the merry-go-round. What is the angular speed of the merry-go-round after Angelica lands on it?
D.) Angelica stays in place while Boris walks back to the edge of the merry-go-round. What is the angular speed of the merry-go-round when he gets there?
a)
using conservation of angular momentum
0.5 M r^2 w1 = (0.5 M r^2 + m r^2) w'
0.5* 200* 8 = ( 0.5* 200 + 50) w'
w' = 5.33 rad/s
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b)
w = 8 rad/s
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c)
again using momentum conservation
I w1 + mvr = (I + mr^2) w'
0.5* 200* 1.5^2 * 8 + 35*6* 1.5 = ( 0.5* 200* 1.5^2 + 35* 1.5^2)w'
w' = 6.963 rad/s
d)
using conservation of angular momentum
(I + ma r^2) w' = ( I + (ma + mb) r^2) w
( 0.5* 200* 1.5^2 + 35* 1.5^2)*6.963 = (0.5* 200* 1.5^2 + ( 35 + 50)* 1.5^2)* wf
wf = 5.081 rad/s
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