Question

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

Answer 1

Answer:

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

Explanation:

The tangential speed experimented by the tack ($v$), measured in meters per second, is equal to the product of the angular speed of the wheel ($\omega$), measured in radians per second, and the distance of the tack respect to the rotation axis ($R$), 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:

$\omega = 2.83\,\frac{rev}{s} \times \frac{2\pi\,rad}{1\,rev}$

$\omega \approx 17.781\,\frac{rad}{s}$

Then, the tangential speed of the tack is: ($\omega \approx 17.781\,\frac{rad}{s}$, $R = 0.393\,m$)

$v = \left(17.781\,\frac{rad}{s} \right)\cdot (0.393\,m)$

$v = 6.988\,\frac{m}{s}$

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