I need a detailed explanation with all work shown please! The Figure shows two k

Question

I need a detailed explanation with all work shown please!

The Figure shows two kids playing in a small playground merry-go-round. At the instant shown, both 20kg kids are standing at the edge of the 2.0m 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 1.3rad/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 0.20m 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 + 2*m*R^2

I1 = ((1/2)*190*2*2) + (2*20*2*2)

I1 = 540 kg m^2

#b) L1 = I1*w1 = 540*1.3 = 702 kg m^2 /s

#c)

KEi = 0.5*I1*w1^2 = 0.5*540*1.3*1.3 = 456.3 J

#d) I2 = (1/2)*M*R^2 + 0 = (1/2)*190*2*2) = 380 kg m^2

#e) Lf = I2*w2

Lf = Li

I2*W2 = I1*W1

w2 = 702/380

w2 = 1.847 rad/s

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