Circular Motion; textbook clarification

In summary, the textbook states that if the wheels and tires of a car are rolling without slipping or sliding, the bottom of the tire is at rest against the road at each instant and the frictional force exerted by the road is static friction. The question arises as to how this is possible since the tires are in constant motion. The answer is that in pure rolling, the vector sum of the velocities at the bottom point is 0, causing the lowermost point to have 0 velocity. This is because the force of the wheel on the ground is counteracted by an equal and opposite force of the ground on the wheel, which only affects the vertical direction. The net velocity is 0 because the velocity due to rotation (wr) canc
  • #1
ThomasMagnus
138
0
Hello,

I am currently studying circular motion. I came across something in my textbook that I would like some helP with.

It says:"if the wheels and tires of a car are rolling normally without slipping or sliding, the bottom of the tire is at rest against the road at each instant; so the frictional force the road exerts on the tires is static friction"

My question is: How could the tires be at rest if they are in constant motion? Wouldn't the frictional force be kinetic since the wheels are moving?

Thanks
 
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  • #2
ThomasMagnus said:
Hello,

I am currently studying circular motion. I came across something in my textbook that I would like some helP with.

It says:"if the wheels and tires of a car are rolling normally without slipping or sliding, the bottom of the tire is at rest against the road at each instant; so the frictional force the road exerts on the tires is static friction"

My question is: How could the tires be at rest if they are in constant motion? Wouldn't the frictional force be kinetic since the wheels are moving?

Thanks

Look at the picture
attachment.php?attachmentid=33145&stc=1&d=1300306422.png


Here the lower most point has 2 velocities ... the green one due to translation and red due to rotation.

As in case of pure rolling, wr=v so lowermost point has 0 velocity

*this will not be true in case of rolling with slipping, as in that case either v>wr or v<wr
 

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  • #3
Hi,

Are you saying the vector sum of the velocities are 0 at the bottom?

Is this because the force the wheel applies to the ground is counteracted by an equal and opposite force of the ground on the wheel?

(I'm really new at this so excuse my ignorance ;)

Thanks
 
  • #4
ThomasMagnus said:
Is this because the force the wheel applies to the ground is counteracted by an equal and opposite force of the ground on the wheel?

These forces will be in vertical direction. how can you expect them to change a horizontal velocity?

vcm is the velocity of each particle towards right, right?
this will b true of the sphere was not rotating and so will remain true even if its ratating

and due to rotation each particle will have speed wr=v in tangential direction ... ie left for lowermost point ...

SO net velocity is v - wr = v -v = 0
 
  • #5
for your help.

Hello,

Thank you for reaching out for clarification on this concept. The statement in your textbook is referring to the fact that the point of contact between the tire and the road is momentarily at rest during each rotation of the tire. This is due to the fact that the tire is rolling without slipping or sliding, meaning that the point of contact is constantly changing as the tire rotates. Therefore, at any given instant, the point of contact between the tire and the road is at rest, even though the tire as a whole is in constant motion. This is why the frictional force is considered to be static in this scenario.

I hope this helps to clarify the concept for you. If you have any further questions, please don't hesitate to ask. Good luck with your studies!
 

1. What is circular motion?

Circular motion is the movement of an object along a circular path. It occurs when an object travels at a constant speed around a central point, known as the center of rotation.

2. What are the key principles of circular motion?

The key principles of circular motion include centripetal force, tangential velocity, and centripetal acceleration. Centripetal force is the force that keeps an object moving in a circular path. Tangential velocity is the speed at which an object is moving tangent to the circular path. Centripetal acceleration is the acceleration towards the center of the circle that keeps an object moving in a circular path.

3. What is the difference between linear and circular motion?

Linear motion is the movement of an object along a straight line, while circular motion is the movement of an object around a circular path. Linear motion follows Newton's first law of motion, whereas circular motion follows Newton's second law of motion.

4. How is circular motion related to the concept of inertia?

In circular motion, the tendency of an object to resist any change in its motion (inertia) is responsible for the object's constant speed along the circular path. It is the inertia of the object that causes it to continue moving in a circular path, even when there is no outward force acting on it.

5. Can an object in circular motion have a constant speed and changing velocity?

Yes, an object in circular motion can have a constant speed and changing velocity. This is because velocity is a vector quantity that takes into account the object's speed and direction of motion. In circular motion, the object's speed may be constant, but its direction of motion is constantly changing, resulting in a changing velocity.

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