Speed and acceleration of a stone in a rotating tire

[Muneerah]

Homework Statement

A tire 0.319 m in radius rotates at a constant
rate of 98.4 rev/min.
Find the speed (relative to the tire’s axle)
of a small stone lodged in the tread on the
outer edge of the tire.
Answer in units of m/s.

Find the acceleration of the stone.
Answer in units of m/s2.

Homework Equations

V=2*pi*r*f
a_c= v²/r

The Attempt at a Solution

I basically solved for the velocity of the tire which is 197.22 m/s
how do you find the relative speed ?? If you could find the velocity I would be able to solve for the acceleration. Thank you

 

[Andrew Mason]

Homework Statement

A tire 0.319 m in radius rotates at a constant
rate of 98.4 rev/min.
Find the speed (relative to the tire’s axle)
of a small stone lodged in the tread on the
outer edge of the tire.
Answer in units of m/s.

Find the acceleration of the stone.
Answer in units of m/s2.

Homework Equations

V=2*pi*r*f
a_c= v²/r

The Attempt at a Solution

I basically solved for the velocity of the tire which is 197.22 m/s
how do you find the relative speed ?? If you could find the velocity I would be able to solve for the acceleration. Thank you

You are calculating the tangential speed of a point on the outer surface of the tire. How does that compare to the speed of the stone?

Check your units. Your answer is not correct. (You are given the rotational speed in revolutions per minute, not seconds).

AM