A horse on a merry-go-round is 20 ft from the center and travels at 10 mph. What is its angular speed?
To find the angular speed of the horse on the merry-go-round, we need to understand the relationship between linear speed and angular speed.
Linear speed is the distance traveled per unit of time, often measured in feet per second or miles per hour. On the other hand, angular speed is a measure of how fast an object rotates around a fixed point, typically measured in radians per second.
The equation that relates linear speed (V) and angular speed (ω) is:
V = ω * r
where V is the linear speed, ω is the angular speed, and r is the radius or distance from the center of rotation.
In this case, the horse on the merry-go-round is 20 ft from the center and travels at 10 mph. We can convert the linear speed from miles per hour to feet per second by multiplying it by 1.47 (since 1 mph is equal to 1.47 ft/s).
Linear speed (V) = 10 mph * 1.47 (ft/s per mph) ≈ 14.7 ft/s
Now we can solve the equation V = ω * r for the angular speed (ω) by rearranging it:
ω = V / r
Substituting the given values, we have:
ω = 14.7 ft/s / 20 ft
ω ≈ 0.735 radians/s
Therefore, the angular speed of the horse on the merry-go-round is approximately 0.735 radians per second.