# Problem with 2 cars on almost masless spining platform

• farolero
In summary, the conversation discusses a scenario involving two cars on a spinning platform and the concept of reference frames. The platform initially has almost zero mass and the cars are aimed radially in opposite directions. As the platform starts to spin, the cars remain still and the net angular momentum is zero. However, when the pilots suddenly turn the cars 90 degrees, the problem arises of what would happen in terms of conservation of energy and momentum. The mentor explains that the frame of reference must be chosen carefully and consistently in order for these quantities to remain conserved. Frame jumping, or switching between different frames of reference, can lead to incorrect conclusions.
farolero
So to cars are in a circular spining platform around its center which weight is so low it can be neglected, the cars initially aim radially in opposite directions.

The cars start moving radially in opposite diractions, notice net angular momentum is zero because the cars are moving radially and the platform is still.

Then suddenly after some time both pilots turn 90º right.

What would happen?

farolero said:
So to cars are in a circular spining platform around its center which weight is so low it can be neglected
You cannot assume zero mass, when you want to apply unbalanced forces / torques to it.

farolero said:
...the platform is still.
So is it initially still or spinning?

farolero said:
What would happen?
Given what you have learned already, what do you think would happen.

I didnt say zero but almost zero which is physically posible.

The platform is initially still.

What i think would happen is that the platform would start spining the opposite sense to the exact speed of the cars so net momentum is zero.

Energy would be conserved taking as a frame reference the platform and momentum would be conserved with a frame reference from an outside obeserver.

But I am still working on frame of reference where the crux of the problem seems to be, I am not very sure what means being an inertial frame of reference.

farolero said:
, I am not very sure what means being an inertial frame of reference
It means a frame of reference where Newton's laws hold. In particular Newton's first law, the law of inertia, which states that objects which are not experiencing an external force travel in a straight line at a constant velocity.

The truth is that some time ago I would doubt conservation of momentum or conservation of angular momentum, But by analisis i think now is totally true.

Ill let you see my doubts:

Theres a one gram platform with two 1 ton cars on it.

The cars are at 100 m radius aiming tangentially.

Initially all system is still.

I start rotating the platform what should be effortless cause the cars won't move just their wheels will.

I keep rotating the platform till the w=1000.

Since the cars are still I employed nearly no energy.

Now i change the frame of reference to the platform

The cars now are going at a speed of v=wr=100*1000=100,000 m/s.

Now both cars suddenly turn 90º.

Do you see my trouble with the frame of reference?

[mentor's note: Some off-topic text has been removed from this post, leaving the question about how conservation of energy works]

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More than I don't understand concerning reference frame and kinetic energy:

There are two 1 kg particles going in opposite sense at 1 m/s.

Energy from a central point=0.5*1*1^2+0.5*1*1^2=1.

But if I set my frame reference in one of the particles then energy=0+0.5*1*2^2=2.

So do you see my problem of obtaining different energies depending the frame reference we take?

farolero said:
More than I don't understand concerning reference frame and kinetic energy:

There are two 1 kg particles going in opposite sense at 1 m/s.

Energy from a central point=0.5*1*1^2+0.5*1*1^2=1.

But if I set my frame reference in one of the particles then energy=0+0.5*1*2^2=2.

So do you see my problem of obtaining different energies depending the frame reference we take?

If that's the whole point, why not start with this simple scenario? And yes, kinetic energy is obviously frame dependent, given it is determined by velocity.

farolero said:
More than I don't understand concerning reference frame and kinetic energy:
...
So do you see my problem of obtaining different energies depending the frame reference we take?

Conservation of energy says that the total energy of a closed system does not change. It does not say that the energy is the same no matter which frame you use, just that whatever frame you choose, it will remain the same. So the idea is that you pick a frame that's convenient for solving the problem, and stick with that throughout the analysis.

Perhaps the simplest example: What is the total energy (kinetic plus potential) of a 1kg mass sitting on a table one meter high? Given that the table is in my living room, 100 meters above sea level? It's ##mgh##, but is ##h## equal to 1 or to 101? Either way I can use conservation of energy to find the kinetic energy of the object when I drop it: one way it is ##(101-100)mg## and the other way it is ##(1-0)mg## and it comes out the same.

farolero
farolero said:
The problem I have now is that I have slight doubts concerning conservation of energy
A quantity that is measured to have the same numeric value no matter what [inertial] reference frame you use when you perform the measurement is called "invariant".

A quantity that remains the same over time in any chosen [inertial] reference frame is called "conserved".

If we consider classical Newtonian mechanics...

Mass is both invariant and conserved. No matter what reference frame you choose, the mass of the object is the same. And no matter how many times you measure that mass, it will remain the same.

Energy, momentum and angular momentum are conserved but are not invariant. They will have different values depending on what reference frame you use when you measure them. But if you stick to one frame, they will remain the same over time.

Volume is invariant but is not conserved. No matter what reference frame you use to measure it, the volume of an object will be the same. But objects can grow or shrink over time. Their volume need not remain the same.

Edit:

If one carelessly switches from using one reference frame to using another reference frame while expecting conserved quantities to remain the same, that is called "frame jumping". It is a common problem encountered by first year physics students.

farolero and Dale
jbriggs444 said:
If one carelessly switches from using one reference frame to using another reference frame while expecting conserved quantities to remain the same, that is called "frame jumping". It is a common problem encountered by first year physics students.

I see that's what i did wrong to solve the original problem ill try again:

I can not take as frame reference the platform cause that would be a rotational reference and that would not be allowed so ill take an outside observer reference:

To keep angular momentum conserved from an outside observer the outside observer will see the cars move radially and then remain still to be the platform the one that is rotating now

To keep energy conserved i conclude all kinetic energy of the car has been converted to heat by friction of the tyres.

Although this last step seems antiintuitive and I have some trouble with it.

farolero said:
To keep energy conserved i conclude all kinetic energy of the car has been converted to heat by friction of the tyres.

Although this last step seems antiintuitive and I have some trouble with it.
This is what happens when you create unphysical problems.

For a disk of any finite mass there is no problem. The smaller the disk, the faster it turns in the end state. Energy is conserved. Some ends in the disk and some in the cars. If you work it out, you will almost certainly find that as the disk gets less and less massive, a greater and greater fraction of the total energy ends up on the disk.

For a disk of zero mass, it ends up turning infinitely fast and the cars end up with no kinetic energy. The energy in the disk is ##0 \times \infty##. That's not defined. Which is a clue that the setup is not physically achievable.

farolero
Well the disk has a mass of 1 gram and can not rotate faster than the cars wheels logically which keeps a constant speed of the wheels with the platform as reference frame:

farolero said:
Well the disk has a mass of 1 gram and can not rotate faster than the cars wheels logically which keeps a constant speed of the wheels with the platform as reference frame:
What makes you think that the cars wheels rotate at a constant rate?

farolero
Because the engine has an inertia as to make variations of speeds in the wheels slow and controlled by the pilot.

The wheels arent massless nor the engine of the car, just the platform is ALMOST masless.

farolero said:
Because the engine has an inertia as to make variations of speeds in the wheels slow and controlled by the pilot.
Well, that's news.

Nobody said that the cars were being driven by an engine. I thought you were working a conservation of energy problem with ideal cars with frictionless, massless wheels that did not need engines.

If the cars have engines and friction then indeed, the lost kinetic energy will manifest in engine braking or in tire friction as you indicated in #11.

farolero
But there's no engine braking the car is going at a constant speed so the wheels rotate a constant speed so the engine rotates at constant speed with respect to the platform.

Im an engine engineer if the engine of a car is going at a constant speed you just need work as to beat friction that at 1 m/s is very low and steering the car 90º as well insignifically brakes the engine, you don't expect a 100% engine brake in a 90º turn

farolero said:
But there's no engine braking the car is going at a constant speed so the wheels rotate a constant speed so the engine rotates at constant speed with respect to the platform.
If you have ever driven a car down a hill, you know that constant speed, constant tire rotation rate and constant engine rotation rate does not mean that there is no engine braking.

[Note that the engine's rotation rate need not be referenced against the platform. Very few modern engines used in automobiles have a vertical crankshaft]

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farolero
Well definitely you puzzled me there.

What if instead of cars we use bicycles.

This experiment could be easily reproduceable you could hang a very light platform from a rotation point in the ceiling and put two kids with bicycles carrying some ballast on the platform.

First you make them go radially and turn 90º and then the opposite, start tangentially and turn 90º to the center and see what happens.

Its not very obvious where energy have gone.

The tyres haven't heat up, there has been no skid mark, no sound, the kids kept pedaling at a constant speed effortless except in the begining...

farolero said:
What if instead of cars we use bicycles.
It does not matter what we use as long as we agree on the rules for how the objects behave.. Are the wheels frictionless? Do they rotate freely? Are they driven and thereby constrained to a fixed speed?

Would you expect that choice to factor into an analysis based on energy conservation?

Everything behaves according you expect from reality.

We just take the freedom of taking a 1 gram platform.

This seems a good example to work on frame of reference and fictitious forces.

edit:

Does the term fictitious energy exist? This would explain pretty well the problem.

farolero said:
Everything behaves according you expect from reality.
We just finished having a disagreement because you did not specify whether the wheels on your cars had friction or were connected to a drive train and an engine with friction that was being driven at a constant rotation rate. Now you want to explicitly fail to specify details in a new scenario.

No. That's not going to work.

Well the details are all according reality and reality is very complex i can't describe absolutely the scenario, in all case confuse it to obtain the answer I want or expect.

Does the term fictitious energy exist? It would fit pretty well here.

The problem would be easily reproduceable and posible to predict what would happen rightly.

jbriggs444 said:
We just finished having a disagreement because you did not specify whether the wheels on your cars had friction or were connected to a drive train and an engine with friction that was being driven at a constant rotation rate. Now you want to explicitly fail to specify details in a new scenario.

No. That's not going to work.

It seems the whole point is to make the scenario unnecessarily complicated and ambiguous. The frame dependence of energy and momentum (which seems to be the whole point) can be shown on much simpler cases, like the one in post #7.

jbriggs444
Yes but at this moment I think its better to complete farther the conservation laws understanding before going to the reference frame.

Two things can happen in my initial problem from an outside observer:

The cyclists simply turn right and in exchange the platform starts spining extreamly fast the opposite sense

Or more intuitively the cyclists remain still and the platform spins slowly the opposite sense

farolero said:
Yes but at this moment I think its better to complete farther the conservation laws understanding before going to the reference frame.
The lack of understanding demonstrated by this remark makes it clear that any further involvement is pointless. I'm out.

farolero said:
i can't describe absolutely the scenario
This is not acceptable. Please PM me with the details requested if you wish to continue this thread.

farolero said:
Does the term fictitious energy exist?.
I have never heard that term used. However, time independent fictitious forces can have an associated potential.

farolero
So there are two ice skaters in the center of a spinning platform.

The ice skaters would accelerate radially to an speed of 1 m/s moment they would both turn 90º right simultaneously.

The weight of the ice skaters would be 100 kg each and the weight of the spinning platform 1 gram.

In this scenario from an outside observer the skaters will end up moving or still?

farolero said:
they would both turn 90º right simultaneously.
Are you assuming that they are "coasting" through the turn, I.e. Doing 0 work with their legs?

Dale said:
Are you assuming that they are "coasting" through the turn, I.e. Doing 0 work with their legs?

Yes they are coasting and doing zero work with their legs.

Then assuming the skates are frictionless on the ice, kinetic energy is conserved. I believe that is the whole point of your setup. You want the skaters to turn while conserving kinetic energy.

So what unknowns do you have, and what constraints and conservation principles can you use?

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I have to keep constant the initial kinetic energy which would be 0.5*200*1=100

And angular momentum that would be zero

So 0=mvr-Iw=200*v*1-iw=0
So 200v=Iw
So supposing the platform has such a shape as to have a moment of inertia equal to 2 then
200v=w

So now i balance energy:
100=0.5*200*v^2+1w^2
100=100v^2+w^2
so 100-100v^2=w^2
substituting:
100-100v^2=40000v^2
so 100=40100v^2
v=0.05 m/s
so w=100

Would this be correct?

The approach is correct. I haven't checked the arithmetic, but even if you made an error there you have the concept right.

## 1. What is the problem with 2 cars on an almost massless spinning platform?

The problem with 2 cars on an almost massless spinning platform is that the platform will experience a significant increase in angular velocity due to the addition of the cars' masses. This can lead to instability and potential accidents.

## 2. How does the mass of the cars affect the spinning platform?

The mass of the cars directly affects the spinning platform by increasing its overall mass and moment of inertia. This results in a higher angular velocity and potential instability.

## 3. Can the problem be solved by adding more cars to the platform?

No, adding more cars to the platform will only exacerbate the problem. The more mass that is added, the higher the angular velocity and instability of the platform will be.

## 4. Is there a way to prevent the problem with 2 cars on an almost massless spinning platform?

One way to prevent this problem is to limit the number of cars on the platform and ensure that their masses are evenly distributed. Another solution is to increase the mass of the spinning platform itself to counterbalance the added mass of the cars.

## 5. What are the potential dangers of the problem with 2 cars on an almost massless spinning platform?

The potential dangers of this problem include accidents and injuries due to the instability of the platform. It can also cause damage to the platform and the cars themselves. Additionally, the added mass and angular velocity of the platform can make it difficult to control and maneuver, posing a risk to anyone operating it.

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