Question

a wheel is rotating at 7 radians per second, and the wheel has a 23 - inch diameter. what is the speed of a point on the rim?
a. 398 ft per min
b. 403 ft per min
c. 393 ft per min
d. 408 ft per min

Explanation:

Step1: Find the radius of the wheel

The diameter \(d = 23\) inches. The radius \(r=\frac{d}{2}=\frac{23}{2}\) inches.

Step2: Use the formula \(v = r\omega\) (where \(v\) is linear speed and \(\omega\) is angular speed)

Given \(\omega=7\) radians per second. So the linear speed in inches per second is \(v = r\omega=\frac{23}{2}\times7=\frac{161}{2}\) inches per second.

Step3: Convert inches per second to feet per minute

• Convert inches to feet: \(1\) foot \( = 12\) inches.
• Convert seconds to minutes: \(1\) minute \(=60\) seconds.

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Answer:

B. \(403\) ft per min