Question

Suppose a wheel with a tire mounted on it is rotating at the constant rate of 3.37 times a second. A tack is stuck in the tire at a distance of 0.387 m from the rotation axis. Noting that for every rotation the tack travels one circumference, find the tack's tangential speed.

Answer 1

Answer:

8.195 m/s

Explanation:

A)Period is given by: T = 1/f where f is frequency. Thus,

Period of time for 1 rev = 1/3.37 = 0.2967s

Now, velocity = distance/time

Distance will be equivalent to the circumference.

Thus,

angular Velocity= Circumference of the Circle/Time; Thus,

ω = d/t = 2πr/t

r is radius and is 0.387m

Thus,

ω = 2π x 0.387/0.2967 = 8.195 m/s

Answer 2

Answer:

The tangential speed of the tack is 8.19 m/s.

Explanation:

The wheel rotates 3.37 times a second that means wheel complete 3.37 revolutions in a second. Therefore, the angular speed ω of the wheel is given as follows:

$\omega =3.37rev/s \times(\frac{2\pi rad}{1s} )\\\\=21.174rad/s$

Use the relation of angular speed with tangential speed to find the tangential speed of the tack.

The tangential speed v of the tack is given by following expression

v = ω r

Here, r is the distance to the tack from axis of rotation.

Substitute 21.174 rad/s for ω, and 0.387 m for r in the above equation to solve for v.

v = 21.174 × 0.387

v = 8.19m/s

Thus, The tangential speed of the tack is 8.19 m/s.