Question

1. determine the angular velocity of a bicycle tire that rotates 90 times per minute? 6.28 rad/s 3.14 rad/s 9.42 rad/s 4.71 rad/s

Explanation:

Step1: Convert rotations per minute to rotations per second

Since there are 60 seconds in a minute, to convert 90 rotations per minute to rotations per second, we divide 90 by 60. So, $\frac{90}{60}= 1.5$ rotations per second.

Step2: Convert rotations to radians

One full - rotation is $2\pi$ radians. To find the angular velocity in radians per second, we multiply the number of rotations per second by $2\pi$. So, $\omega=1.5\times2\pi$. Using $\pi\approx3.14$, we have $\omega = 1.5\times2\times3.14=9.42$ rad/s.

Answer:

$9.42\frac{\text{rad}}{\text{s}}$