Question

1. determine the angular velocity of a bicycle tire that rotates 60 times per minute?

12.57 $\frac{rad}{s}$
1.57 $\frac{rad}{s}$
6.28 $\frac{rad}{s}$
3.14 $\frac{rad}{s}$

Explanation:

Step1: Convert rotations per minute to rotations per second

Since there are 60 seconds in a minute, if the tire rotates 60 times per minute, then the number of rotations per second $n=\frac{60}{60}=1$ rotation per second.

Step2: Convert rotations to radians

One full - rotation is equal to $2\pi$ radians. The angular velocity $\omega$ (in radians per second) is given by $\omega = 2\pi n$. Substituting $n = 1$ into the formula, we get $\omega=2\pi\approx2\times3.14 = 6.28$ rad/s.

Answer:

$6.28\frac{\text{rad}}{\text{s}}$