Question

A wheel with a tire mounted on it rotates at a constant rate of 2.77 times a second. A tack is stuck in the tire at a distance 0.357m from the rotation axis. noting that for every rotation the tack travels one circumference. find the tacks tangential speed.

__________m/s
what is the tacks radial acceleration?
___________m/s^2

Answer 1

6.21 m/s.

108.14 m/s².

Step-by-step explanation:

Using circular motion equation,

Tangential speed, v = w * r

r = radius of rotation

= 0.357 m

w = angular velocity in rad/s

= 2πf

f = frequency

= 2.77 Hz

w = 2π × 2.77

= 17.4 rad/s.

v = 0.357 × 17.4

= 6.21 m/s.

a = v²/r

= r * w^2

= (17.4)^2 * 0.357

= 108.14 m/s²

Answer 2

Tangential speed = 6.22 m/s

Radial acceleration = 108.23 m/s²

Step-by-step explanation:

Tangential speed, v = rw

r = radius of rotation = 0.357m

w = angular velocity = 2πf

f = frequency = 2.77 /s

w = 2π × 2.77 = 17.41 rad/s

Tangential speed = 0.357 × 17.411 = 6.22 m/s

Radial acceleration = v²/r = (6.22²)/0.357 = 108.23 m/s²