Four children stand at edge of a circular horizontal platform that is free to ro

Question

Four children stand at edge of a circular horizontal platform that is free to rotate about a vertical axis. Each child has a mass of 35 kg and are at positions that are a quarter circle from each other. The platform has a moment of inertia equal to 500 kg*m^2 and a radius of 2.0 m. The system is initially rotating at 6.0 rev/min. The children walk toward the center of the platform until they are 0.50 m from the center.

(a) What is the rotational speed of the platform when the children are at the 0.50 m positions?

(b) What is the change in rotational kinetic energy of the system?

Explanation / Answer

Here,

a) let the final angular speed is wf

initial angular momentum = final angular momentum

(500 + 4 * 35 * 2^2) *6 = (500 + 4 * 35 * 0.50^2) * wf

solving for wf

wf = 11.9 rev/s

the final angular speed is 11.9 rev/s

b)

change in rotational kinetic energy = -0.50 * (500 + 4 * 35 * 2^2) *( 6 * 2pi)^2 + 0.50 * (500 + 4 * 35 * 0.50^2) * (11.9 * 2pi)^2

change in rotational kinetic energy = 742221 J

the change in rotational kinetic energy is 742221 J

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