(snip)..... while the point at the bottom in contact with the ground has zero speed for instance.

The point at the bottom in contact with the ground does not have a zero speed if the axle is in motion parrallel to the ground.

While the axle is in motion the wheel is rotating about the axle. There is no interval of time that the axle is in motion that the wheel is motionless to the ground.

The only way the wheel can be motionless to the ground at the ground is IF the axle is motionless compared to the ground.

It doesn't matter how small of an interval of time you measure, if the axle is in motion compared to the ground, the wheel that is in contact with the ground will not remain there during that interval of time UNLESS the axle is motionless for that interval of time.

The point at the bottom in contact with the ground does not have a zero speed if the axle is in motion parrallel to the ground.
If it's not clear from what I said, the point of the wheel in contact with the ground is not moving with respect to the ground at the instant it is in contact with the ground.

If it's not clear from what I said, the point of the wheel in contact with the ground is not moving with respect to the ground at the instant it is in contact with the ground.

Again, you are saying the part of the wheel that is in contact with the ground is motionless. That is a false statement. At NO TIME while the axle is in motion is the wheel motionless at the ground.

Again, you are saying the part of the wheel that is in contact with the ground is motionless. That is a false statement. At NO TIME while the axle is in motion is the wheel motionless at the ground.
So what is the speed of a point on a rolling wheel at the instant it is in contact with the ground?

So what is the speed of a point on a rolling wheel at the instant it is in contact with the ground?

If an interval of time is measured, the part of the wheel that was in contact with the ground traveled a distance greater than zero, as the wheel has an RPM, and is constantly rotating about the axle while at that RPM.

The speed is greater than zero in that interval of time....that is, unless you think time stops at that point?

http://upload.wikimedia.org/wikipedia/commons/6/69/Cycloid_f.gif

One more peep out of motor daddy on this subject means a warning.

http://upload.wikimedia.org/wikipedia/commons/6/69/Cycloid_f.gif

One more peep out of motor daddy on this subject means a warning.

Good, give me a warning, because I'm not budging on this. In your diagram, at no time is the point of the wheel that leaves the red mark trail stationary to the ground. Measure it yourself...

If it takes 1 second to complete one revolution of the wheel, and the wheel is 1 meter in diameter, how far does the point leaving the red mark travel in, say, .00000000000001 seconds? You do plan on measuring the distance it travels in a time interval, don't you??

Are you seriously saying you have no concept of instantaneous velocity?! Go and look up simple harmonic motion.

If an interval of time is measured
No interval of time is being measured. I am talking about the instantaneous velocity of a point on the edge of a rolling wheel. Any measurement of that applying v = \frac{\Delta x}{\Delta t} over a finite time interval only yields an average velocity over that interval, and at best an approximation to the instantaneous velocity at any time within that interval.


that is, unless you think time stops at that point?
I have no idea what you think that's even supposed to mean, and whatever it is, it's clear you're only looking for some excuse to drag in some personal agenda of yours (apparently some issue with instantaneously defined quantities not being directly measurable) that has nothing to do with anything being discussed in this thread.

Are you seriously saying you have no concept of instantaneous velocity?! Go any look up simple harmonic motion.

Are you seriously saying that you can stop time?? There is no such thing as "instantly." Every measure of motion is measured as distance traveled during a duration of time.

Are you seriously saying that you can stop time?? There is no such thing as "instantly." Every measure of motion is measured as distance traveled during a duration of time.

Przyk has explained this to you very well MD and let me tell you quite publicly that I am in no mood to tolerate your trolling. Choose your next post very carefully.

Przyk has explained this to you very well MD and let me tell you quite publicly that I am in no mood to tolerate your trolling. Choose your next post very carefully.

Do the math yourself.

The wheel is 1 meter in diameter.
The wheel completes one revolution per second.

You can not measure a point on the wheel as zero distance traveled unless the time interval measured is zero, because the wheel is in motion.

If you think you can, you're nuts!

Mod note: Motor Daddy has been given a 3 day ban, hopefully to go back to do some reading. Also, off topic posts have been moved from the shape of the relativistic wheel thread

I just noticed this thread....


You can not measure a point on the wheel as zero distance traveled unless the time interval measured is zero, because the wheel is in motion.


Mod note: Motor Daddy has been given a 3 day ban, hopefully to go back to do some reading. Also, off topic posts have been moved from the shape of the relativistic wheel thread

I think a better response would have been to point out that instantaneous = a time interval measured as zero.

Motor Daddy's arguement seemed to me to be consistent in his inclusion of an elapsed time.

Initially my thought was to change the description/discussion, to a tank track, where the motion of the track relative to the ground is more obviously zero, while in contact with the ground, since it occurrs over a measureable period of time.

Your comments are noted.


I think a better response would have been to point out that instantaneous = a time interval measured as zero.

Przyk pointed this out a number of times already. Motor Daddy likes to troll, and this was a perfect example of that.


Motor Daddy's arguement seemed to me to be consistent in his inclusion of an elapsed time.

He was arguing about the validity of having instantaneous anything. He is wrong as any 16 year old who has studied basic dynamics knows.

Every measure of motion is measured as distance traveled during a duration of time.



You can not measure a point on the wheel as zero distance traveled unless the time interval measured is zero, because the wheel is in motion.

Yes, you can not measure but you can calculate.
Speed ​​here is a time-dependent sinus function with a periodicity of 2 pi.

The whole reason wheels are superior to sled runners is that the wheels don't (in normal use) slide against the road. It's why toothed gears are used for precision clockwork. It's why the engine torquing the wheels drives the car forward against the road. It's why icy or oily conditions or hydroplaning results in reduced control of the automobile.

Motor Daddy:

What you say is partly true, but you're missing half the picture.

Any point on the wheel has a constant non-zero speed relative to the axle. But we're talking about a wheel that also has its axle moving along relative to the ground, and we're interested in the speed of the point that is instantaneously at the bottom of the wheel at some time.

For a trolling wheel that is not slipping, the point at the bottom of the wheel is moving "backwards" compared to the direction of motion of the axle. Moreover, it turns out that the speed at which the axle is moving forward (carrying all points on the wheel with it) is precisely equal to the speed at which the bottom of the wheel is moving backwards relative to the axle due to the wheel's rotation. So, when you come to consider the net speed of the point at the bottom of the wheel relative to the road, it is exactly zero.

This is only true at the exact instant where the point is in contact with the road. An instant before or after that, the point has a non-zero velocity.

I also notice that you seem to be struggling with the difference between average velocity, measured over a finite time interval, and instantaneous velocity, measured over an infinitessimal time interval. Perhaps you need to aquaint yourself with the difference between the two concepts.

This isn't even an issue about relativity (which is MD's usual problem), the fact the base of a wheel which isn't slipping is stationary relative to the ground is one of the basic results in classical mechanics for this area. I remember doing it in high school, never mind 1st year of university.

It looks like we can add derivatives to the list of things MD doesn't understand. Not understanding calculus would go a long way to explaining his issues.

I am quiet sure that MD doesn't know any calculus. He struggles with algebra. So, yes, the idea of instantaneous velocity, which is the result of a derivative, is likely to be utterly incomprehensible to him.

Motor Daddy:

What you say is partly true, but you're missing half the picture.

Any point on the wheel has a constant non-zero speed relative to the axle. But we're talking about a wheel that also has its axle moving along relative to the ground, and we're interested in the speed of the point that is instantaneously at the bottom of the wheel at some time.

For a trolling wheel that is not slipping, the point at the bottom of the wheel is moving "backwards" compared to the direction of motion of the axle. Moreover, it turns out that the speed at which the axle is moving forward (carrying all points on the wheel with it) is precisely equal to the speed at which the bottom of the wheel is moving backwards relative to the axle due to the wheel's rotation. So, when you come to consider the net speed of the point at the bottom of the wheel relative to the road, it is exactly zero.

This is only true at the exact instant where the point is in contact with the road. An instant before or after that, the point has a non-zero velocity.

I also notice that you seem to be struggling with the difference between average velocity, measured over a finite time interval, and instantaneous velocity, measured over an infinitessimal time interval. Perhaps you need to aquaint yourself with the difference between the two concepts.

I've never thought of it that way before with the axle being the opposite speed to the base of the wheel. That's extremely useful to use in other materials. Things that people have never used it for like particle field orbits, and space time particle relativity, and Gravity. It made a light go on in my head. :)

People like Motor Daddy shouldn't be banned if it is a useful exercise in covering science.

Motor Daddy, perhaps this will help: throw a ball straight up in the air and watch it return to the ground. The ball essentially started with a positive vertical velocity, reached its apex, then came back down with a negative velocity. It should be obvious that the ball had a velocity of zero but "only for an instant".

It should be obvious that the ball had a velocity of zero but "only for an instant".

His issue is that he cannot imagine an instant short enough to see the ball completely stopped during all points of time during that instant; I think he's missing the definition of "instantaneous" (i.e. something that occurs at a single point in time.)