In: Physics
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?
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,
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