A rotational tire and tape problem.

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    Rotational Tire
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Homework Help Overview

The problem involves a tire rolling along a road without slipping, focusing on the velocity of a piece of tape attached to the tire at different positions relative to the road. The subject area includes concepts of rotational motion and kinematics.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the relationship between the tape's position on the tire and its velocity relative to the road, questioning how the distance from the road affects this velocity. There are inquiries about the velocity of the tape when it touches the road and the velocity of the axle. Some participants attempt to connect the linear velocity to the rotational motion using the equation v = ω × r.

Discussion Status

The discussion is ongoing, with participants offering insights and prompting further exploration of the problem. Some guidance has been provided regarding the relationship between the tape's velocity and the axle's velocity, but no consensus has been reached on the final understanding of the velocities involved.

Contextual Notes

Participants are navigating the complexities of rotational motion and the implications of the tire's rolling without slipping. There is an emphasis on understanding the velocities at different points of the tire, particularly the tape's position at the top and when it contacts the road.

Lazar Trif
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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.
 
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What's the velocity when the tape touches the road? What's the velocity of the axle the tire rotates on?
 
Bystander said:
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?
 
Bystander said:
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.
 
You're getting there --- one more step.
 
Bystander said:
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
 
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?
 
Bystander said:
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!
 
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.
 

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