Did you know that the friction between car tires and the road is static friction, even while the car is moving and the wheels are rotating? As you said " has to do with the fact that the Earth exerts a force only on the part of the tire in contact with the ground, and this part of the tire is momentarily motionless."
This is the basis for anti-lock brake systems (ABS) . Since the maximum static friction force is larger than the kinetic friction force, a car can be stopped fastest if we prevent the wheels from locking up. When the wheels lock up, the friction force is changed to kinetic friction (the tires and the ground are moving with respect to each other) thereby reducing the acceleration and increasing the time and length required to bring the car to a halt.
Note that it is only when kinetic friction is present that the tires and ground are moving with respect to one another.
So far, I agree with you.
So the carters claim that the earth must be accelerated because there is a force on it from the cart is false.
I disagree here. What happened to F = ma?
Static forces do not do any work.
I know what static friction is: it's the friction between two objects that are not in relative motion. I am not sure what you mean by "static force" in general, but from your statement that static forces do no work, I am guessing that it's a force on an object which isn't in motion at all. Is that correct?
So, although both terms include the word "static", static friction might not be a static force. If both the object applying the frictional force and the object to which the frictional force is applied are moving at the same speed, then the friction is static friction, because the two objects are not in relative motion, but it is not a static force, because the object receiving the force is in motion. Such a force does do work.
In fact, what I have proposed (using the ground as the stationary reference for an inertial frame where only the cart and the wind are in motion) is such a common practice that I am amazed at the futile arguments being made against it!
It is common. And as I said here, you can do it if you want. But if you do it, you can't invoke conservation of momentum.
As I said before, 69dodge, I appreciate the open-minded approach you have to the subject. It is a breath of fresh air from the closed minded dogma of the carteers.
Thanks. I try.