A rotational tire and tape problem.

[Lazar Trif]

Homework Statement

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

Homework Equations

v=ω×r

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.

 

[Bystander]

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

 

[Lazar Trif]

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

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?

 

[Lazar Trif]

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

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.

 

[Bystander]

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

 

[Lazar Trif]

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

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

 

[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?

 

[Lazar Trif]

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?

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

 

[haruspex]

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