Suppose a wheel with a tire mounted on it is rotating at the constant rate of 2.69 times a second. A tack is stuck in the tire at a distance of 0.331 m from the rotation axis. Noting that for every rotation the tack travels one circumference, find the tack's tangential speed.

the tack's tangential speed is  5.59 m/s

Explanation:

Given that;

R = 0.331 m

wheel rotates 2.69 times a second which means, the wheel complete 2.69 revolutions in a second, so

ω = 2.69 rev/s × 2π/1s = 16.9 rad/s

using the relation of angular speed with tangential speed

tangential speed v of the tack is expressed as;

v = R × ω

so we substitute

v = 0.331 m × 16.9 rad/s

v = 5.59 m/s

Therefore, the tack's tangential speed is  5.59 m/s