Question

Suppose a wheel with a tire mounted on it is rotating at the constant rate of 2.55 times a second. A tack is stuck in the tire at a distance of 0.357 m from the rotation axis. Noting that for every rotation the tack travels one circumference, find the tack's tangential speed. tangential speed: m / s What is the tack's centripetal acceleration

Answer 1

Step-by-step explanation:

Given:

Time for 1 rev = 1/2.55

= 0.392s

To rad/s,

= 2π/0.392

w = 16.03 rad/s

v = wr

= 16.03 * 0.357

= 5.72 m/s

B.

a = v²/r

= 5.72²/0.357

= 91.72 m/s²

Answer 2

Tangential speed = 5.72 m/s

Centripetal acceleration =
`91.6\text{ m/s}{}^2`

Step-by-step explanation:

The tangential speed, V, is given by

`v=\omega r`

where
`\omega` is the angular speed and is given by
`2\pi f` (f is the angular frequency or frequency of rotation)

Thus,

`v=2\pi f r = 2*3.14*2.55*0.357 = 5.72\text{ m/s}`

The centripetal acceleration,a, is given by

`a=(v^2)/(r)`

`a=(5.72^2)/(0.357) = 91.6\text{ m/s}{}^2`