Suppose a wheel with a tire mounted on it is rotating at the constant rate of 2.83 times a second. A tack is stuck in the tire at a distance of 0.393 m from the rotation axis. Noting that for every rotation the tack travels one circumference, find the tack's tangential speed

The tangential speed of the tack is 6.988 meters per second.

Explanation:

The tangential speed experimented by the tack (), measured in meters per second, is equal to the product of the angular speed of the wheel (), measured in radians per second, and the distance of the tack respect to the rotation axis (), measured in meters, length that coincides with the radius of the tire. First, we convert the angular speed of the wheel from revolutions per second to radians per second:

Then, the tangential speed of the tack is: (, )

The tangential speed of the tack is 6.988 meters per second.