A rotational tire and tape problem.

In summary: This is called the rolling centre. If the wheel is rotating around an axle, then the rolling centre is the axle.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?
  • #1
Lazar Trif
5
0

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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  • #2
What's the velocity when the tape touches the road? What's the velocity of the axle the tire rotates on?
 
  • #3
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?
 
  • #4
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.
 
  • #5
You're getting there --- one more step.
 
  • #6
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
 
  • #7
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
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!
 
  • #9
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.
 

1. What is a rotational tire and tape problem?

A rotational tire and tape problem refers to a physics problem that involves the rotation of a tire or wheel wrapped with a strip of tape. It is a commonly used problem in introductory physics courses to understand concepts such as rotational motion, torque, and angular velocity.

2. How is a rotational tire and tape problem solved?

To solve a rotational tire and tape problem, you need to use the principles of rotational motion, such as the moment of inertia, torque, and angular velocity. The problem usually involves finding the final angular velocity, the tension in the tape, or the acceleration of the tire.

3. What are some real-world applications of rotational tire and tape problems?

Rotational tire and tape problems have practical applications in various fields, such as engineering, mechanics, and sports. For example, understanding rotational motion can help engineers design more efficient machines, while athletes can use it to improve their performance in sports such as discus or hammer throwing.

4. Are there any common misconceptions about rotational tire and tape problems?

One common misconception about rotational tire and tape problems is that the tension in the tape is always equal to the weight of the tire. In reality, the tension can vary depending on the angle at which the tape is wrapped around the tire and the friction between the tire and the ground.

5. What are some tips for solving rotational tire and tape problems?

First, draw a clear diagram to visualize the problem and label all the known and unknown variables. Then, use the relevant equations for rotational motion, such as the rotational analogs of Newton's laws, to set up and solve the problem. It is also helpful to check the units of the final answer to ensure it is in the correct form.

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