Question

# A 5.0-m radius playground merry-go-round with a moment of inertia of 2000 kg?m2 is rotating freely...

A 5.0-m radius playground merry-go-round with a moment of inertia of 2000 kg?m2 is rotating freely with an angular speed of 3.0 rad/s. Two people, each having a mass of 60 kg are standing right outside the edge of the merry-go-round. One person radially steps on the edge merry-go-round with negligible speed and the angular speed changes to ?1. A few seconds later, the second person radially steps on the merry-go-round with negligible speed but at distance of 4.0 m from the axis of rotation (so there are now two people on the merry-go-round) and the angular speed changes to ?2. Determine ?1-?2.

here,

moment of inertia of ground , I = 2000 kg.m^2

radius , r = 5 m

initial angular speed , w0 = 3 rad/s

a)

m1 = 60 kg and r1 = 5 m

let the final angular speed be w1

using conservation of angular momentum

I * w0 = (I + m1 * r1^2) * w1

2000 * 3 = ( 2000 + 60 * 5^2) * w1

the angular speed is 1.71 rad/s

b)

m2 = 60 kg and r2 = 4 m

let the final angular speed be w1

using conservation of angular momentum

I * w0 = (I + m1 * r1^2 + m2 * r2^2) * w2

2000 * 3 = ( 2000 + 60 * 5^2 + 60 * 4^2) * w2

the angular speed is 1.35 rad/s

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