the merry go round music box has a diameter of 12.5 inches. it is scale model of a Hershchell-Spillman Carousel which is 35 feet in diameter. A miniature horse 5.5 inchs from the center of the music box makes one complete rotation in 27 seconds. find the horse's angular speed in radians per second.Round your answer to the nearest hundredth.
the angular speed is 2π/27 radians/second
(all the other pieces of data are irrelevant for the angular speed. If you wanted the horse's linear speed then they would enter the picture.)
To find the angular speed of the miniature horse in radians per second, we first need to convert the units of the given diameter and distance from the center.
1 foot = 12 inches
Given:
Diameter of the Hershchell-Spillman Carousel = 35 feet = 35 * 12 inches = 420 inches
Diameter of the Merry Go Round Music Box = 12.5 inches
Distance of the miniature horse from the center = 5.5 inches
Now, let's calculate the angular speed.
Angular speed is defined as the angle traversed per unit of time. In this case, the miniature horse makes one complete rotation, which is equal to 2π radians, in 27 seconds.
To find the angular speed in radians per second, we need to divide the angle (2π radians) by the time (27 seconds).
Angular speed = 2π radians / 27 seconds
Angular speed ≈ 0.232 radians/second (rounded to the nearest hundredth)
Hence, the horse's angular speed is approximately 0.232 radians per second.