Problem 98

Question

A Ferris wheel has a radius of 25 feet. The wheel is rotating at two revolutions per minute. Find the linear speed, in feet per minute, of a seat on this Ferris wheel.

Step-by-Step Solution

Verified

Answer

The linear speed of a seat on the Ferris wheel is $100\pi$ feet per minute.

1Step 1: Find Angular Speed in Radians

First, convert the angular speed from revolutions per minute to radians per minute. This is done using the conversion factor that one revolution is equal to $2\pi$ radians. Therefore, the angular speed in radians per minute is $2 * 2\pi = 4\pi$ radians per minute.

2Step 2: Apply the Formula for Linear Speed

Now apply the formula for finding the linear speed in circular motion, which is the radius of the circle multiplied by the angular speed in radians. Plugging in the given values, the linear speed is $25 feet * 4\pi$ radians per minute.

3Step 3: Simplify the Result

The result in step 2 simplifies to $100\pi$ feet per minute. This is the linear speed of a seat on the Ferris wheel.

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