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