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# Consider a freely spinning merry-go-round, which can be treated as a uniform disc of radius R and mass m1 rotating about a vertical?

Consider a freely spinning merry-go-round, which can be treated as a uniform disc of radius R and mass m1 rotating about a vertical axis through its center. Initially the merrygo-round is at rest. A boy of mass m2 jumps with a horizontal speed v, landing at A, which is a distance R 4 from the center. Hint: Neglect the vertical fall of the boy.

As the boy is approaching the merry-goround, what is the magnitude of his initial angular momentum with respect to the center of the merry-go-round?

1. Li = m1 vR

2. Li = m2 vR

3. Li = m2 v R/ 2

4. Li = m2 v R/ 4

5. Li = m2 v 3R/ 4

6. Li = m1 vR/ 4

7. Li = m1 v 3R/ 4

8. Li = m1 v R /2

Consider the case where the mass of the boy is the same as the mass of the merry-go-round; i.e., m1 = m2 = m = 47 kg. The radius of the merry-go-round is R = 12 m. The initial velocity of the boy is v = 6 m/s. Hint: Treat the boy and the merry-goround together as an isolated system. Determine the ﬁnal angular velocity of the merry-go-round in radian/sec. Answer in units of radian/sec.

### 1 Answer

- Anonymous2 months agoFavorite Answer
4. Li = m2 v R/ 4

m2*v*R/4 = (½*m1*R² + m2*(R/4)²)*w

for m1=m2=m, mass cancels; R somewhat cancels

v/4 = (R/2 + R/16)*w

4v = (8R+R)*w = 9Rw

w = 4v / 9R

for v=6 R=12

w = 4*6 / 9*12 = 2/9 = 0.22 rad/s

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