Express the angular speed in radians per second.
-A car is traveling at $34 \mathrm { mph }$. If its tires have a diameter of 26 inches, how fast are the car's tires turning? Express the answer in revolutions per minute. If necessary, round to two decimal places.
A) $439.56$ revolutions per minute
B) $2761.85$ revolutions per minute
C) $433.56$ revolutions per minute
D) $879.12$ revolutions per minute

Question

Quizplus · Accepted Answer

First, convert the car's speed from miles per hour to inches per minute: $34 \mathrm{mph} \times 5280 \mathrm{ft/mile} \times 12 \mathrm{in/ft} \times \frac{1}{60} \mathrm{min/hr} = 36288 \mathrm{in/min}$. The circumference of a tire is $\pi d = \pi \times 26 \mathrm{in}$. The number of revolutions per minute is the total distance traveled per minute divided by the circumference of a tire: $\frac{36288 \mathrm{in/min}}{\pi \times 26 \mathrm{in}} \approx 439.56$ revolutions per minute.

Express the Angular Speed in Radians Per Second 34mph34 \mathrm { mph }34mph

Express the Angular Speed in Radians Per Second $34 \mathrm { mph }$