Question

A spin balancer rotates the wheel of a car at 500 revolutions per minute. If the diameter of the wheel is 26 inches, what road speed is being tested?
a. 26 rad/s
b. 3.2 rad/s
c. 52 rad/s
d. 81 rad/s​

Answer 1

Answer:

c. 52 rad/s

Step-by-step explanation:

Final question does not correspond with available option. The real question is: What is the angular speed in radians per second?

At first we assume that spin balance rotates at constant rate and convert given angular speed, measured in revolutions per minute, into radians per second:

$\omega = \left(500\,\frac{rev}{min} \right)\cdot \left(2\pi\,\frac{rad}{rev} \right)\cdot \left(\frac{1}{60}\,\frac{min}{sec} \right)$

$\omega \approx 52.360\,\frac{rad}{s}$

Which corresponds to option C.