Question

5. A 3.0 m diameter merry-go-round (mass 200 kg) is spinning at 10 rpm. A child of 30.0 kg runs tangent to the merry-go-round at 2.0 m/s, in the opposite direction that it is turning, and jumps onto the outer edge. Calculate the merry-go-round's angular velocity, immediately after the child jumps on.

Answer 1

here,

the mass of merry-go-round , m1 = 200 kg

diameter , d = 3 m

radius , r = d/2 = 1.5 m

the initial angular velocity of merry-go-round , w0 = 10 rpm = 1.05 rad/s

the mass of child , m2 = 30 kg

the initial speed of child , u = 2 m/s

let the final angular velocity of the merr-go-round be w

using conservation of angular momentum

(0.5 * m1 * r^2) * w0 - m2 * v * r = (0.5* m1 * r^2 + m2 * r^2) * w

(0.5 * 200 * 1.5^2) * 1.05 - 30 * 2 * 1.5 = ( 0.5 * 200 * 1.5^2 + 30 * 1.5^2) * w

solving for w

w = 0.5 rad/s

the merry-go-round's angular velocity is 0.5 rad/s