Three children are riding on the edge of a merry‑go‑round that has a mass of 105 kg and a radius of 1.40 m . the merry‑go‑round is spinning at 20.0 rpm. the children have masses of 22.0, 28.0, n 33.0 kg. if the 28.0 kg child moves to the center of the merry‑go‑round, what is the new angular velocity in revolutions per minute?

new angular velocity  is 25.20 rpm

Explanation:

Given data

mass = 105 kg

radius =  1.40 m

spinning = 20.0 rpm

masses = 22.0 , 28.0 and 33.0 kg

to find out

new angular velocity

solution

we apply here conservation momentum

L initial  = L final   1

we know Ip = 1/2 mr² = 1/2 × 105 ×1.4² = 102.9 kg/m³

and for children initial I(i) = ( 33 + 28 + 22 )=   83 × 1.4² = 162.68 kg/m²

and  I(f) children final = 33+ 22 = 55 × 1.4² = 107.80 kg/m²

so as that from equation 1

Ip  + I(i) × 20 = Ip ×  I(f)  × ω

(102.9  + 162.68 ) × 20 = (102.9 +  107.80 ) × ω

ω =  25.209302

so  new angular velocity  is 25.20 rpm