Question

A 23.0 kg child is riding a playground merry-go-round that is rotating at 40.0 rpm. What centripetal force, in N, must she exert to stay on if she is 1.00 m from its center?
What centripetal force, in N, does she need to stay on an amusement park merry-go-round that rotates at 3.00 rpm if she is 6.90 m from its center?
Compare each force with her weight.

Answer 1

Use Fc = m ω^2 r with ω = (rpm)(2π/60).

1) 40.0 rpm, r = 1.00 m:
ω = 40(2π/60) = 4π/3 ≈ 4.189 rad/s
Fc = 23.0(4.189^2)(1.00) ≈ 4.04×10^2 N ≈ 404 N

2) 3.00 rpm, r = 6.90 m:
ω = 3(2π/60) = π/10 ≈ 0.31416 rad/s
Fc = 23.0(0.31416^2)(6.90) ≈ 15.7 N

Compare with her weight: W = mg = 23.0(9.80) = 225 N.
- At 40.0 rpm: Fc ≈ 404 N ≈ 1.79 W (179% of her weight).
- At 3.00 rpm: Fc ≈ 15.7 N ≈ 0.0696 W (≈ 7.0% of her weight).