Question

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?

Answer 1

new angular velocity is 25.20 rpm

Step-by-step 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