You have a plane and a conveyor belt.

[NanoStuff]

Originally posted by: mugs

Originally posted by: PurdueRy

Originally posted by: mugs

Listen carefully... the conveyor belt cannot hold the plane in place. Not in this physical world. It can't. So IF the conveyor belt is trying to match the wheel's speed, there WILL be some lag. It is impossible for the conveyor belt to match the speed of the wheel while the plane is moving relative to the ground next to the conveyor belt. In order for the conveyor belt to even BEGIN to move, the plane has to move relative to the ground next to the treadmill, because the plane cannot make its wheels rotate like a car does. So if the treadmill catches up instantaneously, you'll have instantaneous infinite acceleration.

The conveyor belt simply cannot hold the plane in place, not without defying the laws of physics. The situation described in the OP's question is impossible.

Actually the situation in the OP is fine. As he said "The speed the wheels move FORWARD" This direction implies linear speed. It was when he added a follow up post of his own incorrect interpretation that all this confusion came about. The question is if the treadmill matched the forward speed of the aircraft....that is all. The OP agreed this situation causes takeoff. Therefore the answer is YES

He phrased it two different ways in the OP. No wonder people are discussing two different questions.

Version 1:

The belt compensates for the rotation of the wheels in reverse

Version 2:

as in the belt moves in reverse exactly as fast as the wheels move forward.

Those mean the opposite.

At least we can all agree that DLeRium is a pompous ass.

Yes, like I said, that was my mistake . My intention was to only give one scenario but the words came together all wrong. I double checked the consistency before I posted, but even so I blew it. I would have edited the post but by the time I noticed the problem, the thread advanced too far into a spiral of doom. If I edited at that point, people would be battling it out because the thread was edited, but now they can at least examine the original question as it was originally stated.

But then again now that people realize there are alternative interpretations, it's interesting to examine them both.

 

[AlienCraft]

Originally posted by: NanoStuff
The plane increases it's thrust and the wheels begin to rotate. The belt compensates for the rotation of the wheels in reverse, as in the belt moves in reverse exactly as fast as the wheels move forward.

And if it matters, it's a nice sunny day and you have good tires, so you get perfect traction on the belt at all times. Your plane also happens to be very powerful and you can give it as much thrust as you like, but the source of thrust is at the back of the plane so it never provides airflow over the wing.

Does the plane take off?

Since there is no inherent airflow over the wings, it will never take off.
Jets do not suck air over the wings the push it through space. Propellors, on the other hand , would draw air across the wing surface and it would.

 

[PurdueRy]

Originally posted by: AlienCraft

Originally posted by: NanoStuff
The plane increases it's thrust and the wheels begin to rotate. The belt compensates for the rotation of the wheels in reverse, as in the belt moves in reverse exactly as fast as the wheels move forward.

And if it matters, it's a nice sunny day and you have good tires, so you get perfect traction on the belt at all times. Your plane also happens to be very powerful and you can give it as much thrust as you like, but the source of thrust is at the back of the plane so it never provides airflow over the wing.

Does the plane take off?

Since there is no inherent airflow over the wings, it will never take off.
Jets do not suck air over the wings the push it through space. Propellors, on the other hand , would draw air across the wing surface and it would.

You still don't get it. The engines will not provide airflow over the wings. The plane WILL move forward however, which does provide airflow over the wings. Draw the FBD of the situation and you will see a unopposed force in the forward direction. This causes acceleration relative to air.

 

[AlienCraft]

A lot of you guys SUCK at critical thinking and reading comprehension.
As well as a basic understanding of aerodynamics.

As far as wings are concerned , Jets PUSH, Propellors PULL.

 

[PurdueRy]

Originally posted by: AlienCraft
A lot of you guys SUCK at critical thinking and reading comprehension.
As well as a basic understanding of aerodynamics.

As far as wings are concerned , Jets PUSH, Propellors PULL.

I wouldn't make such claims...you are just setting yourself to be nominated...if you get my point.

 

[AlienCraft]

Originally posted by: Evadman

Originally posted by: JMWarren
I'm still not so sure. If the plane isn't moving forward in space there is no air flow over the wings.

The point is the plane is moving. the wheels do nothing. The belt moving backwards means nothing, since the plane uses it propeller or jet engine to push against the air not the ground.

Plane != Car

No one eliminated gravity from the equation. The only thing the conveyor belt eliminates is the friction holding the plane stationary and motionless.
Since the ground must be stationary in order to induce airflow over the wings (The result of the movement through space) if there is no movement through space AND the thrust is at the rear so there is no inherent airflow over the wing. No movement, No Airflow, no lift, no flight.

 

[NanoStuff]

Originally posted by: AlienCraft

Originally posted by: NanoStuff
The plane increases it's thrust and the wheels begin to rotate. The belt compensates for the rotation of the wheels in reverse, as in the belt moves in reverse exactly as fast as the wheels move forward.

And if it matters, it's a nice sunny day and you have good tires, so you get perfect traction on the belt at all times. Your plane also happens to be very powerful and you can give it as much thrust as you like, but the source of thrust is at the back of the plane so it never provides airflow over the wing.

Does the plane take off?

Since there is no inherent airflow over the wings, it will never take off.
Jets do not suck air over the wings the push it through space. Propellors, on the other hand , would draw air across the wing surface and it would.

A plane doesn't use the airflow over the wing provided by it's propulsion to fly. That airflow is provided by translational velocity, aka forward speed.

 

[PurdueRy]

Originally posted by: AlienCraft

Originally posted by: Evadman

Originally posted by: JMWarren
I'm still not so sure. If the plane isn't moving forward in space there is no air flow over the wings.

The point is the plane is moving. the wheels do nothing. The belt moving backwards means nothing, since the plane uses it propeller or jet engine to push against the air not the ground.

Plane != Car

No one eliminated gravity from the equation. The only thing the conveyor belt eliminates is the friction holding the plane stationary and motionless.
Since the ground must be stationary in order to induce airflow over the wings (The result of the movement through space) if there is no movement through space AND the thrust is at the rear so there is no inherent airflow over the wing. No movement, No Airflow, no lift, no flight.

Like I said before, draw the FBD...see the unopposed force...therefore it accelerates and moves through air. Your concept that the plane remains stationary is incorrect.

 

[NanoStuff]

AlienCraft, are you referring to the translational or angular velocity interpretation of the question? In the former, I disagree... the plane would take off. In the latter I agree, the plane would not take off... although a prop plane might.

 

[waggy]

you know why it does not take off? it has the jenny craig people onit!

 

[AlienCraft]

Originally posted by: PurdueRy

Originally posted by: AlienCraft

Originally posted by: NanoStuff
The plane increases it's thrust and the wheels begin to rotate. The belt compensates for the rotation of the wheels in reverse, as in the belt moves in reverse exactly as fast as the wheels move forward.

And if it matters, it's a nice sunny day and you have good tires, so you get perfect traction on the belt at all times. Your plane also happens to be very powerful and you can give it as much thrust as you like, but the source of thrust is at the back of the plane so it never provides airflow over the wing.

Does the plane take off?

Since there is no inherent airflow over the wings, it will never take off.
Jets do not suck air over the wings the push it through space. Propellors, on the other hand , would draw air across the wing surface and it would.

You still don't get it. The engines will not provide airflow over the wings. The plane WILL move forward however, which does provide airflow over the wings. Draw the FBD of the situation and you will see a unopposed force in the forward direction. This causes acceleration relative to air.

If,in the example above, the conveyor is moving at the same force in opposite of the engines, how does airflow exist with no movement?
The air is not flowing over the wing by virtue of any movement. The force of gravity (the weight of the plane) is still in the same direction, which is down.
An airfoil can only work if there is movement over its surface, and in the original problem, the engines do not provide any airflow over the wings.
No one mentioned a rotary winged aircraft which would be a possibility of
Therefore ,with no movement forward to provide air movement over the wings to provide a force to counter GRAVITY, there will be no lift.
This example assumes that the conveyor is "perfect" and can match the physical forces provided by the jet.
The only way that your example can be correct is with a Chemical ROCKET motor, which would provide a perfect thrust curve, which a jet cannot provide

 

[PurdueRy]

Originally posted by: AlienCraft

Originally posted by: PurdueRy

Originally posted by: AlienCraft

Originally posted by: NanoStuff
The plane increases it's thrust and the wheels begin to rotate. The belt compensates for the rotation of the wheels in reverse, as in the belt moves in reverse exactly as fast as the wheels move forward.

And if it matters, it's a nice sunny day and you have good tires, so you get perfect traction on the belt at all times. Your plane also happens to be very powerful and you can give it as much thrust as you like, but the source of thrust is at the back of the plane so it never provides airflow over the wing.

Does the plane take off?

Since there is no inherent airflow over the wings, it will never take off.
Jets do not suck air over the wings the push it through space. Propellors, on the other hand , would draw air across the wing surface and it would.

You still don't get it. The engines will not provide airflow over the wings. The plane WILL move forward however, which does provide airflow over the wings. Draw the FBD of the situation and you will see a unopposed force in the forward direction. This causes acceleration relative to air.

If,in the example above, the conveyor is moving at the same force in opposite of the engines, how does airflow exist with no movement?
The air is not flowing over the wing by virtue of any movement. The force of gravity (the weight of the plane) is still in the same direction, which is down.
An airfoil can only work if there is movement over its surface, and in the original problem, the engines do not provide any airflow over the wings.
No one mentioned a rotary winged aircraft which would be a possibility of
Therefore ,with no movement forward to provide air movement over the wings to provide a force to counter GRAVITY, there will be no lift.
This example assumes that the conveyor is "perfect" and can match the physical forces provided by the jet.
The only way that your example can be correct is with a Chemical ROCKET motor, which would provide a perfect thrust curve, which a jet cannot provide

Why do you assume its not moving? The force the conveyor belt applies can only apply a torque to the wheels...it cannot provide a countering force to the plane itself to cancel the force of the engine.

 

[Armitage]

Originally posted by: AlienCraft
Since there is no inherent airflow over the wings, it will never take off.
Jets do not suck air over the wings the push it through space. Propellors, on the other hand , would draw air across the wing surface and it would.

Originally posted by: AlienCraft
A lot of you guys SUCK at critical thinking and reading comprehension.
As well as a basic understanding of aerodynamics.

As far as wings are concerned , Jets PUSH, Propellors PULL.

LMAO - nope, you suck at critical thinking. Whether you push or pull completely irrelevent. A propeller can push (hence the term "pusher prop") - take a look at a B-36. And a jet provides airflow in front of it as well as behind - where do you think the air going out the back came from? The only engine that wouldn't would be a rocket.

Regardless, all of that is icompletely irrelevent because thew airflow provided by the engines is does not provide the lift needed to take off. If it did, we wouldn't need runways, all aircraft would be VTOL.

But I don't know what your point is - the airflow over the wings provided (or not) by the engines would be completely unchanged whether there was a conveyor or not. So what is you point?

What all that airflow from the engines does is provide thrust, which is not countered by any force other then those encountered on a routine takeoff. So the plane would roll down the conveyor, with the wheels turning twice as fast as they normally would , and the plane takes off.

 

[MidNiteMysT]

Originally posted by: cKGunslinger

Originally posted by: MidNiteMysT
damn.... is this question really that hard?

the plane wont take off. the only way planes are able to lift off is because of the lift on the wings. thats why they have those huge runways to take off. if it was possible to take off with just a conveyor belt, dont you think airports would be using them? it would be extremely convient. and not only that, dont you think aircraft carriers would use them with their limited space? they dont use them and you cant use them because it wont work. thats why they rely on a "sling shot" type method to get their planes off the ground. this topic so so damn long and it doesnt make sense. if youre running on a tredmel, do you feel air blowing past you? no you dont. and thats why a plane cant lift off. he needs air to pass by its wings. otherwise, why would a plane have wings if it could lift without air passing its wings?

this topic should have been done a loooong time ago.

*sigh* Another moron in the thread who didn't read past the 3rd post.

The plane *moves!* Do you not see that? The plane moves just as if it were on solid ground. Therefore it takes the same length of runway to achive lift off, so turning the 300yd asphalt runways into 300yd conveyor belts would be a bit pointless, don't ya think?

No one is claiming that the plane stays completely motionless, then magically takes off after some period.

THE ROTATING TREADMILL ACTS ON THE FREE-SPINNING WHEELS ONLY AND DOES NOT STOP THE FORWARD MOTION OF THE PLANE PROVIDED BY ITS JETS. THE END.

Now, everyone else who can't see this and think you know something special, please stfu.

that was a pretty cute reply but sadly, it was worthless cause youre a dumbass. the whole point of using a runway to achieve take off is because air is passing by its wings! if you stay pretty much motionless in the same area, air isnt passing you by unless its wind. and you need more than wind to achieve lift. i thought i already explained this to you. if youre running on a treadmill, do you feel air passing by you? NO. so how can a plane take off without air passing its wings? it makes a huge different if youre going down a 300ft runway and 300ft conveyorbelt that keeps you in the same position. i provided so many examples already. and if you in fact are correct about conveyor belts, try responding to my examples such as air craft carriers and a more effiecent use of space in every airport in the world? so i dont know what the hell youre trying to say, but you obviously arent saying it right. nice touch leaving a image with stfu, NERD. maybe you wanna call me a troll too, like a super nerd? hahaha. youre so pathetic. next time, try to not be such a loser.

 

[PurdueRy]

Originally posted by: MidNiteMysT

Originally posted by: cKGunslinger

Originally posted by: MidNiteMysT
damn.... is this question really that hard?

the plane wont take off. the only way planes are able to lift off is because of the lift on the wings. thats why they have those huge runways to take off. if it was possible to take off with just a conveyor belt, dont you think airports would be using them? it would be extremely convient. and not only that, dont you think aircraft carriers would use them with their limited space? they dont use them and you cant use them because it wont work. thats why they rely on a "sling shot" type method to get their planes off the ground. this topic so so damn long and it doesnt make sense. if youre running on a tredmel, do you feel air blowing past you? no you dont. and thats why a plane cant lift off. he needs air to pass by its wings. otherwise, why would a plane have wings if it could lift without air passing its wings?

this topic should have been done a loooong time ago.

*sigh* Another moron in the thread who didn't read past the 3rd post.

The plane *moves!* Do you not see that? The plane moves just as if it were on solid ground. Therefore it takes the same length of runway to achive lift off, so turning the 300yd asphalt runways into 300yd conveyor belts would be a bit pointless, don't ya think?

No one is claiming that the plane stays completely motionless, then magically takes off after some period.

THE ROTATING TREADMILL ACTS ON THE FREE-SPINNING WHEELS ONLY AND DOES NOT STOP THE FORWARD MOTION OF THE PLANE PROVIDED BY ITS JETS. THE END.

Now, everyone else who can't see this and think you know something special, please stfu.

that was a pretty cute reply but sadly, it was worthless cause youre a dumbass. the whole point of using a runway to achieve take off is because air is passing by its wings! if you stay pretty much motionless in the same area, air isnt passing you by unless its wind. and you need more than wind to achieve lift. i thought i already explained this to you. if youre running on a treadmill, do you feel air passing by you? NO. so how can a plane take off without air passing its wings? it makes a huge different if youre going down a 300ft runway and 300ft conveyorbelt that keeps you in the same position. i provided so many examples already. and if you in fact are correct about conveyor belts, try responding to my examples such as air craft carriers and a more effiecent use of space in every airport in the world? so i dont know what the hell youre trying to say, but you obviously arent saying it right. nice touch leaving a image with stfu, NERD. maybe you wanna call me a troll too, like a super nerd? hahaha. youre so pathetic. next time, try to not be such a loser.

Its already been explained a gagillion(thats the correct number) times in this thread. The plane will MOVE on the conveyor belt. We are not saying the plane will accelerate on a conveyor belt while staying in place...we are saying it will physically MOVE FORWARD. This is due to the unopposed force the engines create. All the treadmill does is spin the wheels faster.

Think of the ideal case. You put a toy car on a treadmill. Turn on the treadmill and the toy car will roll in place because the wheels are free to spin. If you apply even a small force with your finger(simulating the engine) the car moves forward. If this force is constant, then the plane/car will accelerate. Thereby taking off.

Hopes this clears up things for ya

 

[kevinthenerd]

Originally posted by: blahblah99
For all the dumbasses that don't think the plane will go anywhere, go look up F=MA. Draw the free body diagram of all the forces acting on the plane and you will see why the plane will take off. In fact, just do it for the horizontal axis and you will see the plane will accelerate.

Now quit arguing, cause it's obvious you guys didn't pay attention or take physics in school.

I can put this problem into a state-space model, but there's no point in doing that if some of you can't even understand F=MA.

F=ma, but you also have to consider Fr=I*alpha (rotational force)

The force goes into rotating the wheels.

Consider the plane itself without the wheels first: In the x-direction, you have a force provided by the thrust in the positive direction, but you have a force provided by the wheels in the negative direction.

How do the wheels push against the plane? You have to draw a second FBD of the wheels for that:

Summation of forces in the x direction yields a negative force by the belt (on the bottom) and a positive force by the plane (on the central axle). The entire couple moment goes into accelerating the wheel in a rotational manner since translational movement was given as zero in the problem (assuming the interpretation of "rotational movement").

Hence, the belt would have to violently accelerate in order to keep the plane from moving, but it's theoretically possible to have a stationary plane in a frictionless setup.

 

[kevinthenerd]

Originally posted by: JujuFish

Originally posted by: NanoStuff
Where the thrust comes from is irrelevant, a car would behave the same way on the conveyor belt. The origin of the power is irrelevant if the wheels hold traction with the belt.

So, so very wrong.

A car with its wheels locked would be accelerated backwards on the conveyor, yes, but there's almost bit of truth to what NanoStuff was saying.

You see, if a car was on a belt, and if you assume that its torque band is constant for any given speed and that it experiences no friction and that the wheels weigh nothing, its real acceleration (in relation to the ground) would be the same regardless if it was a on a belt or not. It's F=ma. If the belt travels backwards, you can just subtract the belt speed from the spedometer and you'll find the real speed.

When you accelerate a body on a frictionless surface, you're only fighting the inertia of the body, which is only dependent on its mass.

 

[kevinthenerd]

Originally posted by: JujuFish

Originally posted by: NanoStuff

Originally posted by: mugs

Originally posted by: NanoStuff
Well then, I don't need to go further than page 14. This Tom fella is correct. If the wheels rotate forward at speed x and the belt rotates backwards at speed x, the outcome is quite obvious that the wheel would remain stationary to an observer regardless of what is attached to it and what force induced rotation on that wheel. If wheel rotation is x(2) and belt speed is x; as would be the case if the belt matched the speed of the plane, the plane would be capable of accelerating forward and thus taking off, but would require approximately twice the power to do so.

Right there you proved you don't know jack ****** about physics.

You proved you have no argument, I win.

No, actually, mugs was quite correct in his assessment.

Yes, F=ma

 

[kevinthenerd]

Originally posted by: mugs

Originally posted by: NanoStuff

Originally posted by: mugs

Originally posted by: NanoStuff
Well then, I don't need to go further than page 14. This Tom fella is correct. If the wheels rotate forward at speed x and the belt rotates backwards at speed x, the outcome is quite obvious that the wheel would remain stationary to an observer regardless of what is attached to it and what force induced rotation on that wheel. If wheel rotation is x(2) and belt speed is x; as would be the case if the belt matched the speed of the plane, the plane would be capable of accelerating forward and thus taking off, but would require approximately twice the power to do so.

Right there you proved you don't know jack ****** about physics.

You proved you have no argument, I win.

Haha... I have to waste my time proving that crap wrong?

I'll let someone else do it for me:
http://www.school-for-champions.com/science/friction_changing_sliding_hard.htm

Fr = µ*N

where

Fr is the resistive force of friction,
µ is the coefficient of friction for the two surfaces (Greek letter "mu"), and
N is the normal or perpendicular force pushing the two objects together.

Where is speed in that equation? It's not there. Friction in the wheels does not depend on the speed it is rotating, it only depends on whether or not it IS rotating.

Not to mention air resistance, which DOES depend on speed, would not be substantially affected by the wheels rotating twice as fast.

For the most simple cases of surface mechanics, you can assume Coulomb friction, but I have to warn you that rolling friction is by no means Coulomb-based. The material deflection usually decreases as you increase speed for a variety of reasons.

 

[kevinthenerd]

Originally posted by: jagec

Originally posted by: JujuFish

Originally posted by: NanoStuff
Speed is not in the equation because a friction coefficient is static, just like any other coefficient. This value is multiplied by a variable quantity, that is the speed of the wheels. You should at the very least understand your own argument

There is a coefficient for static friction as well as one for rolling friction.

Correction: DYNAMIC friction. There is no such thing as "rolling" friction. A wheel in a no-slip condition experiences rolling resistance, which is basically the hodgepodge of forces that act against a moving round object, such as bearing friction, the force absorbed in the deformation of a rubber tire, the energy wasted in rolling over a nonuniform surface, and so on. Friction at the road-tire contact patch is necessary to ensure a no-slip condition, but it has virtually no effect on the dynamics of a freely rotating tire. Static/dynamic friction only comes into play when braking or cornering (or, if the wheel is powered, accelerating).

Even rolling resistance can be awfully negligible under certain conditions, such as a smooth steel wheel rolling over another smooth, hard surface.

Rolling friction is very real, and it occurs due to rigid body mechanics. It's negligible in most cases, but when you say that a belt compensates 1:1 for the rotation of the wheels, you need to look for any tiny amount of force possible to prevent an infinite acceleration of the belt to satisfy such a conditon.

 

[jagec]

Originally posted by: kevinthenerd

You see, if a car was on a belt, and if you assume that its torque band is constant for any given speed and that it experiences no friction and that the wheels weigh nothing, its real acceleration (in relation to the ground) would be the same regardless if it was a on a belt or not. It's F=ma. If the belt travels backwards, you can just subtract the belt speed from the spedometer and you'll find the real speed.

I hope when you say "ground" you mean "conveyor".

 

[kevinthenerd]

Originally posted by: NanoStuff
Unless you disagree that the plane would not move forward even if the belt is moving backwards at the rotational speed of the wheels, in which case I'd like you to explain how this is possible.

If you factor rotational inertia, rolling resistance, etc., combined with a rapidly accelerating belt, it's possible to theoretically satisfy such a conjecture.

 

[kevinthenerd]

Originally posted by: JujuFish

Originally posted by: NanoStuff

Originally posted by: JujuFish

This value is multiplied by a variable quantity, that is the speed of the wheels.

Wrong.

Right.

We can go back and forth saying "Wrong" "Right' for a million years. If you cannot make a counter-argument, you'd be best off observing the conversation rather than participating in it.

Why should I argue this when it has already been done so? Let me quote mugs.

Fr = µ*N

where

Fr is the resistive force of friction,
µ is the coefficient of friction for the two surfaces (Greek letter "mu"), and
N is the normal or perpendicular force pushing the two objects together.

Where is there anything related to the speed of the wheels there?

µ is a function of the speed of the wheels, but it's not that important.

 

[kevinthenerd]

Originally posted by: Adam8281
Yes, of course the plane would take off - and here's another way to envision it:

Suppose a plane is flying through the air at 500 mph. Suppose, also, that there is a 10 mile long treadmill up in the air which is spinning 500 mph in the opposite direction of the plane's movement. And suppose the flying plane can fly over the treadmill and touch its wheels upon it, while continuing to have its engines going. What would happen? Would the treadmill stop the plane when the 500 mph plane touched its wheels to it? No, of course not. Instead, the plane would continue to fly at 500 mph, and its wheels would be spinning at 1000 mph (500 mph in reaction to the spinning treadmill beneath it + 500 mph because the plane is moving at 500 mph.) The treadmill would not STOP the plane because the source of the plane's movement is not the WHEELS but the ENGINES. A plane can travel 500 mph even if its wheels are spinning at 1000 mph or 0 mph. This is unlike a car, which only can travel at 60 mph when its wheels are moving at 60 mph, because the source of a car's movement is the wheels.

Consider, again, the mile-high treadmill example, but this time imagine the treadmill is spinning in the SAME DIRECTION as the plane, but at 8000 mph. Say the plane flew over the treadmill and had its wheels touch the treadmill? Would the plane get an amazing power boost, and hit 8000 mph? No, of course not, instead it would continue to travel at 500 mph while it's wheels started spinning like mad tops and probably disentegrate.

That assumes that the belt doesn't compensate for the rotational movement of the wheels. We need to stop here and realize that this problem's two interpretations have two different answers.

 

[kevinthenerd]

Originally posted by: NanoStuff

Originally posted by: Adam8281
Yes, of course the plane would take off - and here's another way to envision it:

Suppose a plane is flying through the air at 500 mph. Suppose, also, that there is a 10 mile long treadmill up in the air which is spinning 500 mph in the opposite direction of the plane's movement. And suppose the flying plane can fly over the treadmill and touch its wheels upon it, while continuing to have its engines going. What would happen? Would the treadmill stop the plane when the 500 mph plane touched its wheels to it? No, of course not.

Yes, yes it would. Not instantly because the wheels cannot accelerate to 500mph rotation in an infinitely short period of time, the wheels would initially skid on the belt (just like a jet coming in for landing where there is a rubbery screeching sound and more often than not a puff of smoke behind the tires), but in short time the belt would absorb all momentum of the plane.

No, the wheels would accelerate to the point where they'd only absorb part of the momentum. You'd conserve energy:

(1/2)*(mass of the plane)*(speed of the plane initially)^2 = (1/2)*(rotational inertia of the wheels)*(rotational speed of the wheels finally)^2 + (1/2)*(mass of the plane)*(speed of the plane finally)^2 + energy lost due to that friction when the wheels hit