Activity 9C-2 (part 2) A 50 kg merry-go-round can be modeled as a solid disk wit

Question

Activity 9C-2 (part 2) A 50 kg merry-go-round can be modeled as a solid disk with radius 4.0 m The merry-go-round can spin about its axis with negligible friction. A 30 kg child stands at the outer edge of the merry-go-round as shown in the over head view figure to right. Initially, the child and merry-go-round are stationary. The child begins to walk about the perimeter of the merry-go- round and at a later moment in time, the child's velocity is 0.75 m/s, upward in the figure shown. What is the direction of the child's angular momentum vector at this moment in time? a. over-head view b. At this moment in time, what must be the direction of the angular momentum vector of the merry-go-round? in what manner (if at all) does the merry-go-round spin? Explain. c. Two students are discussing their results to the previous question: Student 1: I think that the merry-go-round doesn't move because it's the child that's moving, not the merry go-round. Student 2: Well, what about conservation ofangular momentum, if the child's angular momentum goes from zero to non-zero, doesn't that mean that the merry-go-round's angular momentum ought change too? Do you agree or disagree with either or both of these students? Briefly explain your reasoning . 27 d. Calculate the angular velocity of the merry-go-round.

Explanation / Answer

angular momentum L = m*(r x v )

r is laong x axis ( i )

v is along y axis ( j )

r x v = i x j = k

out of page

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(b)

Into the page

the merry go spins clockwise

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(c)

student 2

momentum before walking Li = 0

momentum after walking Lf = Lmerry + Lchild

from angular momentum conservation , total angular momentum is conserved

Lf = Li

Lmerry + Lchild = 0

Lmerry = -Lchild

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(d)

Lmerry = I*w = (1/2)*M*r^2*w

Lchild = m*v*r

(1/2)*50*4^2*w = 30*0.75*4

w = 0.225 rad/s

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