Suppose a wheel with a tire mounted on it is rotating at the constant rate of 2.23 2.23 times a second. A tack is stuck in the tire at a distance of 0.379 m 0.379 m from the rotation axis. Noting that for every rotation the tack travels one circumference, find the tack’s tangential speed
Question
Explanation:
The given data is as follows.
Angular velocity ([tex]\omega[/tex]) = 2.23 rps
Distance from the center (R) = 0.379 m
First, we will convert revolutions per second into radian per second as follows.
= 2.23 revolutions per second
= [tex]2.23 \times 2 \times 3.14 rad/s[/tex]
= 14.01 rad/s
Now, tangential speed will be calculated as follows.
Tangential speed, v = [tex]R \times \omega[/tex]
= 0.379 x 14.01
= 5.31 m/s
Thus, we can conclude that the tack’s tangential speed is 5.31 m/s.