The Figure shows two kids playing in a small playground merry-go-round. At the i

Question

The Figure shows two kids playing in a small playground merry-go-round. At the instant shown, both 22kg kids are standing at the edge of the 2.18m radius merry-go-round. Treat the merry-go-round as a disk of mass 190kg. At the instant shown, the merry-go-round is rotating at 1.28rad/s.

(a) What is the original total moment of inertia of the system made up of the merry-go-round and children?

(b) What is the angular momentum of the system at the instant shown?

(c) What is the kinetic energy of the system at the instant shown?

The kids run towards the pole and hold it. At this new position, they center is 0.22 m away from the center.

(d) What is the new moment of inertia of the system?

(e) What is the final angular speed of the system?

Explanation / Answer

a) I1 = ((1/2)*M*R^2 + (m*R^2) = ((1/2)*190*2.18*2.18)+(22*2.18*2.18)

b) L = I1*w1 = 556.0308*1.28 = 711.719424 kg m^2 /s

c) KE = 0.5*I1*w1^2 = 455.50043136 J

d) I2 = (1/2)*M*R^2 = ((1/2)*190*2.18*2.18) = 451.478 kg m^2

e) L2 =I2*w2

L2 = L1

451.478*w2 = 711.719424

w2 = 1.575 rad/s

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