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Chapter 4: Problem 64

A carousel with a 50 -foot diameter makes 4 revolutions per minute. (a) Find the angular speed of the carousel in radians per minute. (b) Find the linear speed (in feet per minute) of the platform rim of the carousel.

Short Answer

Expert verified
The angular speed of the carousel is \(8蟺\) radians per minute and the linear speed of the platform rim is \(200蟺\) feet per minute.

Step by step solution

01

Find the angular speed

The carousel makes 4 revolutions per minute. Given that one revolution is equivalent to \(2蟺\) radians (the circumference of a circle in radians), the angular speed 蠅 in radians per minute of the carousel is calculated as: 蠅 = Number of revolutions * \(2蟺\) = 4 * \(2蟺\) = \(8蟺\) radians per minute.
02

Calculate the radius

The diameter of the carousel is given as 50 feet. The radius is half the diameter. So, the radius r = Diameter / 2 = 50 / 2 = 25 feet.
03

Determine the linear speed

The linear speed V of an object moving in a circular path is calculated by multiplying the radius r of the circle by the angular speed 蠅. Therefore, V = r * 蠅 = 25 feet * \(8蟺\) radians per minute = \(200蟺\) feet per minute.

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