Suppose a wheel with a tire mounted on it is rotating at the constant rate of 3.33 times a second. A tack is stuck in the tire at a distance of 0.309 m from the rotation axis. Noting that for every rotation the tack travels one circumference, find the tack's tangential speed

Given:

Angular velocity, w = 3.33 times a second

= 1 rev in 3.33 s

w = 1/3.33

= 0.3 rev/s

Comverting from rev/s to rad/s;

0.3 rev/s * 2pi rad/1 rev

= 1.89 rad/s

Radius, r = 0.309 m

tangential velocity, v = w * r

= 1.89 * 0.309

= 0.583 m/s

Answer: 6.47m/s

Explanation:

The tangential speed can be defined in terms of linear speed. The linear speed is the distance traveled with respect to time taken. The tangential speed is basically, the linear speed across a circular path.

The time taken for 1 revolution is, 1/3.33 = 0.30s

velocity of the wheel = d/t

Since d is not given, we find d by using formula for the circumference of a circle. 2πr. Thus, V = 2πr/t

V = 2π * 0.309 / 0.3

V = 1.94/0.3

V = 6.47m/s

The tangential speed of the tack is 6.47m/s