Sorry Aleks, I was just fooling around. I agree with you on all points. I was just taking a radical skeptic point of view... in which almost nothing can be absolutely proved or known.
I'm no physicist. But when they don't stop with the pavement, there is no traction. The tires spin. This is why, for example, a drag racer tries very hard not to spin the tires during the race. The drag racer wants to apply just enough power to allow for that "stoppage" of the tire to the pavement so that car is propelled forward. If the power applied by the motor is too much, that power to the tires overcomes the amount of friction that is possible between a rubber tire and the pavement, at which point that "stoppage" cannot happen, the tires spin, and the racer loses the race.
Wormholes and time travel Aichelburg, P. C. Abstract Already Einstein (1914) worried that his theory of relativity might allow for spacetimes with so-called closed timelike curves. Gödel (1949) constructed a cosmological model where this phenomena can happen, however at the cost of an enormous amount of energy for the journey. More recently renewed interest focussed on the possibility of constructing such time machines with the help of ``wormholes.'' Wormholes are spacetimes with nontrivial topology in which a kind of tunnel exists connecting distant parts in the universe. These wormholes may not only serve as shortcuts in space but also for timetravel. Two important theorems about wormhole spacetimes are known: Hawking (1992) in his paper on ``Chronology projection conjecture'' showed, loosely speaking, that for the construction of a time machine one necessarily needs to violate the energy conditions. Friedman et al. (1993), on the other hand, proved a ``topology protection theorem'' by which it is impossible, under certain assumptions, to probe the nontrivial topology, i.e., travelling or sending light rays through the wormhole from the asymptotic region. Neither of these theorems applies to our construction: Hawking's theorem refers to spacetimes where closed causal curves exist from a certain time on (or up to a certain time), while our solution is an eternal time machine. Friedman's conclusion requires that spacetime is globally hyperbolic, a requirement which is not met by our construction. Whether or not this is physically acceptable is open. .
Yes, I've been down that road and thought about it that way for a long time. But it is surprising how simple the solution is mathematically. The road surface of the tire - the outside diameter - is moving as fast as the car is moving. For every rotation of the tire, the car has to advance the same distance as the circumference of the tire; provided that the tire hasn't lost traction. So we can do simple addition of velocities to prove the solution. The top of the tire is moving at the rotational speed of the tire, in addition to the forward velocity of the car. The bottom of the tire is moving at the velocity of the car minus the rotational velocity of the tire. Since the rotational velocity is equal to the speed of the car, the top of the tire is moving at twice the speed of the car. The bottom of the tire is moving the opposite direction as the car, so the sum of the speeds is zero.
This gets into the relativistic addition of velocities. How it happens is easy to conceptualize if you consider contracted lengths measured by the astronauts in motion, relative to the earth frame of reference. When the astronaut measures the speed of something moving away from them, like a missile they fired, they measure the speed as the distance moved divided by time, lets say in feet per second. But one foot for them is not one foot for us. What they see as a foot, we might see as 2 inches, So in effect, the object travels farther in their frame of reference than it does in ours. Of course their clocks are also running slowly, which is why we both agree on the speed of light even though it covers different distances in the two frames of reference. Turns out that you add the velocities V1 and V2 like you normally would, but then divide by a modifier, as shown below.
If that can be taken as a synonym for "angular" in this context... ...I don't see how the two can be quantitatively compared. Not relative to the road it isn't, or the whole idea falls apart; so what is it moving relative to that's of interest here? Nonzero scalars never sum to zero, AFAIK. If you mean to say the linear velocities of the points at the top and bottom are equal and opposite, again, that can't be true in a frame where the road is still.
No, angular refers to angles. I am talking about the tangential velocity of the outermost radius of the tire. That's why I didn't say angular. Yes is it. The tires are spinning wrt to the car. How fast is it spinning? Show me the math. Yes, I wasn't being particular about the language for simplicity. You really have to consider the vectors. But I also specified that the bottom of the tire is moving the opposite direction of the car, wrt to the car. Sorry you didn't understand that part but I justified ignoring the vectors.
Said another way, however many feet per second the car is moving forward, is the number of feet per second of tire surface, that passes over the point of contact with the road.
Then you've contradicted your initial premise, and the whole thing falls apart. No. If the car defines the reference frame, it's not moving, so it has no direction; and no point on the tire is ever stationary.
The answer is found in the second law of thermodynamics, the law of increasing entropy. Entropy not only applies by default to motion, it also applies to functional complexity and available information. Philosophically, no effect can transcend its cause. In other words, you cannot get out more than is put in, that goes not only for motion; it also applies to functional complexity and available information.
You are just confused. For example, you complained about vectors when I specifically stated that you have to subtract the speed of the tire surface from the forward motion of car. If you understood vectors, you would understand that this compensated for using vectors and instead used the speed. If you don't understand, then ask instead of arguing. It shows more intelligence. And the tire is in motion wrt to the car. Stop tossing around words you don't understand.
However, this is not a case of getting more out than you are putting in. It is a case of ignoring losses. So while you are correct that it would violate the second law, your philosophical interpretation applies more to the first law.
I didn't ignore loses due to friction, gravity and the like, I just didn't see a need to beat a dead horse so to speak. The 2nd law alone blows the proposition completely out. Enough said.
Somebody sure as hell is. This is nothing but an attempt to divert attention from the point at issue, which is your claim that the bottom of the tire is in motion WRT the road. Actually there's nothing intelligent about asking someone who obviously doesn't understand himself. And I never said or implied otherwise, obviously. Sure, like I'm the one who thinks an object that's motionless in a given reference frame has a direction in that frame.
To put a finer point on it, in a frame where the road is still, any given point P on the tread is indeed moving backwards relative to the car when it's moving slower than car, but it cannot be moving in the opposite direction of the car.
No, they are not. That's a ridiculous assumption. Of course frictional forces are dependent on contact area. If there is no contact area, there is no friction.
It's not an assumption. It is the physics we've known for over 500 years. https://en.wikibooks.org/wiki/Physics_Study_Guide/Normal_force_and_friction The magnitude of the force due to friction is the coefficient of friction multiplied by the magnitude of the force normal to the surface. Note that the area does not factor into the answer. If there is no contact, there is no force normal to the surface. [here normal means the force is perpendicular to all vectors in the plane. Leonardo da Vinci made the first experiments on friction using a rectangular block sliding on a dry, flat surface. His main observations are that: 1) the friction force is independent of the area of the surfaces in contact. 2) the friction force is proportional to the applied load. https://www2.virginia.edu/ep/SurfaceScience/friction.html
I have heard on a few occasions how people sometimes buy an air conditioner and don't want to have it mounted in the window or can't, so they just set in the living room. Why does it fail?
Addendum: Wide tires do typically have more traction than narrow tires; not because they are wider, but because they can use softer material by making the tire wider.
Things shrink when they get cold and expand when they get hot. While this is generally true, it isn't always true. Can you name a very common example where this statement fails?
Not sure that works for any source of friction. I know it doesn't work for friction between a fluid and a solid (aka air resistance). It does work for the friction of an object on a surface.
