a wheel is rotating at 7 radians per second, and the wheel has a 23 - inch diameter. what is the speed of a…

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. [ \begin{align*} v&=\frac{161}{2}\times\frac{60}{12}\text{ ft/min}\ &=\frac{161\times60}{2\times12}\text{ ft/min}\ &=\frac{9660}{24}\text{ ft/min}\ & = 402.5\text{ ft/min}\approx403\text{ ft/min} \end{align*} ]

Answer:

B. (403) ft per min