Question

The horse on a carousel is 4.5 m from the central axis. if the carousel rotates at 0.14 rev/s , how long does it take the horse to go around twice?

Answer 1

Answer:

The horse takes 14.29 seconds long to go around the carousel twice.

Step-by-step explanation:

The first thing we have to notice is that if we draw a line from the horse to the center of the carousel, all points over that line will take the same time to go around one, twice, or as many rounds they want.

It is like a clock, where the minute arrow go around the clock, and every point in the arrow hits the 12 at the same instant.

With this in mind, we notice that the distance from the central axis is irrelevant for the problem.

Then, is just that we have the angular velocity of the horse, and the angle the horse makes equals the angular velocity times the time

$\theta=\omega t$

Then, clearing t, and taking into account that the angle is 2 rev, we have that

$t=\frac{\theta}{\omega}=\frac{2 rev}{0.14rev/s}=14.29s$

wich is the answer to our problem.

Answer 2

$\dfrac{ 2 \textrm{ rev}}{0.14 \textrm{ rev/sec}} = \dfrac{100}{7} \textrm{ sec} = 14.3 \textrm{ sec}$