Question

Suppose a wheel with a tire mounted on it is rotating at the constant rate of 2.59 times a second. A tack is stuck in the tire at a distance of 0.329 m from the rotation axis. Noting that for every rotation the tack travels one circumference, find the tack's tangential speed.__________m/s
what is the tacks radial acceleration?
___________m/s^2

Answer 1

Answer:

Tangential speed=5.4 m/s

Radial acceleration=$88.6m/s^2$

Explanation:

We are given that

Angular speed=2.59 rev/s

We know that

1 revolution=$2\pi rad$

2.59 rev=$2\pi\times 2.59=5.18\pi=5.18\times 3.14=16.27 rad/s$

By using $\pi=3.14$

Angular velocity=$\omega=16.27rad/s$

Distance from axis=r=0.329 m

Tangential speed=$r\omega=16.27\times 0.329=5.4m/s$

Radial acceleration=$\frac{v^2}{r}$

Radial acceleration=$\frac{(5.4)^2}{0.329}=88.6m/s^2$