Question

A simple carousel consists of a flat circular floor that rotates a revolution of 12 s.
a) Calculate all the forces acting on a person standing 4.5 m from the center of the carousel. The person weighs 55 kg.
b) What is the shortest lap time the carousel can have without the person starting to slide? The friction figure between the person's shoes and the floor is 0.45.

Answer 1

(a)

$W=mg=55\cdot9.81\approx540(N)$

$F_c=m\omega^2r=m\cdot\frac{4\pi^2}{T^2}\cdot r=55\cdot\frac{4\pi^2}{12^2}\cdot 4.5=68(N)$

(b)

$m\cdot\frac{4\pi^2}{T^2}\cdot r=\mu mg\to T=\sqrt\frac{4\pi^2r}{\mu g}=\sqrt\frac{4\cdot3.14^2\cdot4.5}{0.45 \cdot 9.81}=6.3(s)$