Question

In: Physics

A merry go round (a disk I=(1/2) MR2, M=200 kg, R=2.0 m) rotates initially at 0.3...

A merry go round (a disk I=(1/2) MR2, M=200 kg, R=2.0 m) rotates initially at 0.3 rad/s. A child of mass 40 kg is dropped onto the merry go round at a distance of 1.5 m from the axis of rotation. How fast is the child moving after it comes to turn with the merry go round?

Solutions

Expert Solution

Mass of the merry-go-round = M = 200 kg

Radius of the merry-go-round = R = 2 m

Moment of inertia of the merry-go-round = I

I = 400 kg.m2

Initial angular speed of the merry-go-round = 1 = 0.3 rad/s

Mass of the child = m = 40 kg

Distance of the child from the axis of rotation = L = 1.5 m

Angular speed of the merry-go-round after the child comes to turn with the merry-go-round = 2

By conservation of angular momentum,

2 = 0.245 rad/s

Speed of the child after it comes to turn with the merry-go-round = V

V = 0.37 m/s

Speed of the child after it comes to turn with the merry-go-round = 0.37 m/s


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