Question

A teenager pushes tangentially on a small hand-driven merry-go-round and is able to accelerate it from rest to a frequency of 14 rpm in 10.9 s . Assume the merry-go-round is a uniform disk of radius 2.0 m and has a mass of 670 kg , and two children (each with a mass of 30 kg ) sit opposite each other on the edge.

a.) Calculate the torque required to produce the acceleration, neglecting frictional torque.

b.) What force is required at the edge?

Answer 1

First calculate α

now ω0 = 0 and ω = 14*2π/60 = 1.465 rad/s

so ω = ω0 + α*t

so α = 1.465/10.9 = 0.1344 rad/s^2

τ = I*α

τ = [1/2*M*R^2 + 2*m*r^2]*α

τ = [1/2*670*2^2 + 2*30*2^2]*0.1344

τ = 212.352 N-m

F = τ/R

F = 212.352N-m/2m

F = 106.176N