# C6M.6 A certain playground merry-go-round is essentiallyan iron disk of radius R and mass m. Two children, whosemasses are each m, are originally sitting on opposite sidesof the disk near its outer edge. The merry-go-round isturning essentially without friction around a vertical axisonce every 5 s. The children then clamber toward eachother until each is only R from the center. How long doesit take the merry-go-round to complete a revolution now?(Hint: Model the children as particles.)

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Step 1

Given information:

Radius of the iron disk = R

Mass of the disk = m

Distance of each child from the centre initially = R

Mass of each child = (2/5) m

Initial time taken by the disk to make one rotation (T) = 5 s

Let the initial, moment of inertia and angular velocity = I1, ω1

Let the final, moment of inertia and angular velocity = I2, ω2

Step 2

Hence the initial moment of inertia is given by:

Step 3

Now, according to law of conservation of angular momen...

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