You have two friends which both has a mass of 55 kg. Your friends get onto the e

Question

You have two friends which both has a mass of 55 kg. Your friends get onto the edge of a playground merry-go-round which has a diameter of 3 m and has an unknown mass or moment of inertia and is initially at rest. You push tangentially along one edge of the merry-go-round with a constant force of 200 Newtons for 4.06 seconds.

Inertia of merry-go-round is 141 kg*m^2

The merry-go-round (and your friends) is now rotating at a constant angular speed of 3.14 radians/sec. As your friends move towards the center of the merry-go-round it goes faster and faster. When they both reach a distance of 0.5 m from the center, what is the new angular speed of the merry-go-round?

Explanation / Answer

using angular momentum conservation(I) ,

(141 + 2 x 55 x 1.52 ) x 3.14 = (141 + 2 x 50 x 0.52 )

166 = 388.5 x 3.14

= 7.35 rad/s

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