# A rotational tire and tape problem.

1. Dec 28, 2014

### Lazar Trif

1. The problem statement, all variables and given/known data

A tire is rolling along a road, without slipping, with a velocity v. A piece of tape is attached to the tire. When the tape is opposite the road (at the top of the tire), it's velocity with respect to the road is
2. Relevant equations
v=ω×r

3. The attempt at a solution
Well the tape is 2*radius away from the road, but how does this relate it to the linear velocity.

2. Dec 28, 2014

### Bystander

What's the velocity when the tape touches the road? What's the velocity of the axle the tire rotates on?

3. Dec 28, 2014

### Lazar Trif

The questions is as worded. The tape is at the top of the tire. What is it's velocity when it is at the top of tire, relative to the road?

4. Dec 28, 2014

### Lazar Trif

The velocity of the tape would be 0 when it touches the road. The velocity of the axle would just be a linear velocity of v.

5. Dec 28, 2014

### Bystander

You're getting there --- one more step.

6. Dec 28, 2014

### Lazar Trif

Well I understand I'm missing that one more step, I just mentally can't grasp what it is. The tape is 2r away.... v= w * r

7. Dec 28, 2014

### Bystander

If the tape isn't moving when it touches the road, it's moving "v" less than the axle; if it's opposite that point it will be moving how fast relative to the axle, and in which direction?

8. Dec 28, 2014

### Lazar Trif

v and positively, meaning its velocity relative to the road would be 2v. Thanks!

9. Dec 29, 2014

### haruspex

It can be useful to realise that as a wheel rolls the centre of rotation, at any given instant, is the point of contact with the road.