Question

A merry go round (a disk I=1/2MR^2, M=200 kg, R=2 m) rotates at 0.4 rad/s. A child with a mass of 60 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? A) 0.16 m/s B) 0.30 m/s C) 0.45 m/s D) 0.66 m/s

Answer 1

Using conservation of the angular momentum

I₁W₁ =(I₁+I₂)W ....1

Here I₁=MR²/2 =200*2²/2=400 Kg m² , I₂ =mr² =60*1.5² =135 kg m² (Assume child is point particle.) ,W₁ =0.4 rad/s

so put these value in equation 1

W=400*0.4/(400+135)

W=0.299 rad/s

V=Wr =0.299*1.5 =0.4485

V=0.45 m/s Answer (c)