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

Tangential speed=5.4 m/s

Radial acceleration=
`88.6m/s^2`

Step-by-step explanation:

We are given that

Angular speed=2.59 rev/s

We know that

1 revolution=
`2\pi rad`

2.59 rev=
`2\pi* 2.59=5.18\pi=5.18* 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* 0.329=5.4m/s`

Radial acceleration=
`(v^2)/(r)`

Radial acceleration=
`((5.4)^2)/(0.329)=88.6m/s^2`