Question

A wheel with a tire mounted on it rotates at a constant rate of 2.89 times a second. A tack is stuck in the tire at a distance 39.1cm 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

(A) Tangential speed will be equal to 7.09 m/sec

(B) Radial acceleration will be equal to
`128.5629rad/sec^2`

Step-by-step explanation:

We have given angular speed of the wheel
`\omega =2.89rev/sec=2.89* (2\pi rad)/(sec)=18.149rad/sec`

Radius of the track r = 39.1 cm = 0.391 m

(A) Tangential speed will be equal to
`v=\omega r`, here
`\omega` is angular speed and r is radius

So tangential speed
`v=18.149* 0.391=7.09m/sec`

So tangential speed will be equal to 7.09 m/sec

(B) Radial acceleration will be equal to
`a=(v^2)/(r)=(7.09^2)/(0.391)=128.5629rad/sec^2`

So radial acceleration will be equal to
`128.5629rad/sec^2`