Question

Question1:playground merry-go-round has mass of 75kg and a radius of 3 m. A 25kg child sits on the merry-go-round 2/3's of way out from center.What's the moment of inertia of the merry-go-round/child system?

Question2:On the playground merry-go round in the previous question,one child pushes it CCW with a force of 20 N, while the 25 kg child drags her feet through a hole 2/3 of the way out from the center,causing a CW force of 17 N. What's angular acceleration of the merry-go-round?

Answer 1

Mass of the merry-go-round = M = 75 kg

Radius of the merry-go-round = R = 3 m

Mass of the child = m = 25 kg

Distance of the child from the center of the merry-go-round = d = 2R/3 = 2 m

Moment of inertia of the system = I

Moment of inertia of the system is equal to the moment of inertia of the merry-go-round about it's center plus the moment of inertia of the child(point mass) about the center of the merry-go-round.

I = MR²/2 + md²

I = (75)(3)²/2 + (25)(2)²

I = 437.5 kg.m²

Force applied by the child to push the merry-go-round CCW = F₁ = 20 N

CW Force applied by the child sitting on the merry-go-round = F₂ = 17 N

Net torque on the merry-go-round = T

T = F₁R - F₂d

T = (20)(3) - (17)(2)

T = 26 Nm

Angular acceleration of the merry-go-round =

I = T

(437.5) = 26

= 5.94 x 10^-2 rad/s²

1) Moment of inertia of the system = 437.5 kg.m²

2) Angular acceleration of the merry-go-round = 5.94 x 10^-2 rad/s²