Express the angular speed in radians per second.
-A pick-up truck is fitted with new tires which have a diameter of 41 inches. How fast will the pick-up truck be moving when the wheels are rotating at 415 revolutions per minute? Express the answer in miles per hour rounded to the nearest whole number.
A) 51 miles per hour
B) 8 miles per hour
C) 56 miles per hour
D) 25 miles per hour

Question

Quizplus · Accepted Answer

First, convert the diameter to radius: 41 inches / 2 = 20.5 inches. Convert inches to feet for the radius: 20.5 inches / 12 = 1.7083 feet. The angular speed in radians per second is given by $ \omega = 2\pi \times \text{RPM} / 60 $, where RPM is revolutions per minute. Here, $ \omega = 2\pi \times 415 / 60 \approx 43.633 $ radians per second. To find the linear speed, use $ v = \omega \times r $, where $ v $ is the linear speed in feet per second and $ r $ is the radius in feet. So, $ v = 43.633 \times 1.7083 \approx 74.57 $ feet per second. Convert feet per second to miles per hour: $ 74.57 $ feet/second $\times$ 3600 seconds/hour / 5280 feet/mile $\approx$ 51 miles per hour.

Express the Angular Speed in Radians Per Second