Instantaneous Axis of Rotation

[e(ho0n3]

I have some doubts on the following:

When a wheel rolls without slipping, the point of contact of the wheel with the ground is instantaneously at rest. It is sometimes useful to think of the motion of the wheel as pure rotation about this "instantaneous axis". Points [on the wheel] close to the ground have a small linear speed, as they are close to this instantaneous axis, whereas points farther away have a greater linear speed.

The above is from my Giancoli physics book and accompanying the above is a picture of a bicycle wheel with the top part of the wheel blurred due to the greater speed. I understand what is happening here but I can't help to think that if all parts of the wheel aren't moving with the same speed then wouldn't the wheel suffer from some deformation? I'm guessing if the speed is relatively small, the deformation is ignorable.

Any comments?

 

[Doc Al]

If all parts of the wheel aren't rotating with the same angular speed, then you'll have deformation. Perhaps that's what you are thinking of?

I don't see the problem with a rolling wheel. The linear velocity of any part with repect to the ground is the vector sum of its velocity with respect to the center (same speed for a given radius, but different directions!) plus the velocity of the center with respect to the ground (a constant, presumably). I'm sure you realize that the velocity w.r.t. the center of each part of the wheel points in a different direction.

Does that help at all?

 

[e(ho0n3]

I don't see the problem with a rolling wheel. The linear velocity of any part with repect to the ground is the vector sum of its velocity with respect to the center (same speed for a given radius, but different directions!) plus the velocity of the center with respect to the ground (a constant, presumably). I'm sure you realize that the velocity w.r.t. the center of each part of the wheel points in a different direction.

Yes, this is all perfectly clear.

If all parts of the wheel aren't rotating with the same angular speed, then you'll have deformation. Perhaps that's what you are thinking of?

Have you ever seen a drag race? When the light turns green and the drag racer accelerates, you can see that the wheels acquire an elliptical shape. But I guess this occurs because the wheels are slipping. I guess I'm misinterpreting the cause of the blur on the picture of the bike wheel.

Thanks

 

[Doc Al]

Have you ever seen a drag race? When the light turns green and the drag racer accelerates, you can see that the wheels acquire an elliptical shape. But I guess this occurs because the wheels are slipping.

Ah... now I think I see what you are talking about. For the car to accelerate, frictional force must be exerted on the tire (and, vice versa, on the road). There is no way to do this without some distortion of the tire. (Good observation.)

But I don't think that has anything to do with the picture in your book, which I'm sure just shows a wheel rolling without slipping. Once it's up to speed, no further frictional force is needed (ideal case, of course). The top is probably blurred just to give you the feel that it's moving with respect to the ground (and the observer), while the bottom is unblurred because it's not moving. Makes sense to me.

 

[alio]

"instantaneously" the wheel is rotating about a fixed axis(which is the common point btw the wheel and the ground), so the equation for this case is V=W R, where W is constant and R is variable so when u go far from the "IC" the velocity will increase