Question

A playground merry-go-round with a radius of 1.80 m has a mass of 120 kg and is rotating with an angular speed of 0.350 rev/s. What is its angular speed after a 36.5-kg child gets onto it by grabbing its outer edge? The child is initially at rest.

Answer 1

Answer:

1.64 rad/s

Explanation:

Given,

radius of merry-go-round, r = 1.80 m

mass of  merry-go-round, M = 120 Kg

angular speed, ω = 0.350 rev/s

Initial angular speed = 2π x 0.350 = 2.12 rad/s

Mass of child, m = 36.5 Kg

Moment of inertia of the  merry-go-round

$I = \dfrac{1}{2}Mr^2$

$I = \dfrac{1}{2}\times 120\times 1.8^2$

$I = 349.92\ kg.m^2$

L= I ω = 349.92 x 2.12 = 769.41 kgm²/s

Child moment of inertia

I₂ = m r^2 = 36.5 x 1.8² = 118.26 kg.m²

Final moment of inertia,

I_f = 349.92+118.26 = 468.18 kg.m²

Final speed = $\dfrac{769.41}{468.14}$

$\omega_f = 1.64 \rad/s$

angular speed of the child is equal to 1.64 rad/s