# B Problem with 2 cars on almost masless spining platform

1. Dec 14, 2016

### 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?

2. Dec 14, 2016

### A.T.

You cannot assume zero mass, when you want to apply unbalanced forces / torques to it.

So is it initially still or spinning?

3. Dec 14, 2016

### Staff: Mentor

Given what you have learned already, what do you think would happen.

4. Dec 14, 2016

### farolero

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

5. Dec 14, 2016

### Staff: Mentor

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.

6. Dec 14, 2016

### farolero

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 wont 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]

Last edited by a moderator: Dec 14, 2016
7. Dec 14, 2016

### farolero

More than I dont 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?

8. Dec 14, 2016

### A.T.

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.

9. Dec 14, 2016

### Staff: Mentor

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.

10. Dec 14, 2016

### jbriggs444

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.

11. Dec 14, 2016

### farolero

I see thats 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.

12. Dec 14, 2016

### jbriggs444

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.

13. Dec 14, 2016

### 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:

14. Dec 14, 2016

### jbriggs444

What makes you think that the cars wheels rotate at a constant rate?

15. Dec 14, 2016

### 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.

16. Dec 14, 2016

### jbriggs444

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.

17. Dec 14, 2016

### farolero

But theres 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 dont expect a 100% engine brake in a 90º turn

18. Dec 14, 2016

### jbriggs444

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]

Last edited: Dec 14, 2016
19. Dec 14, 2016

### 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 havent heat up, there has been no skid mark, no sound, the kids kept pedaling at a constant speed effortless except in the begining...

20. Dec 14, 2016

### jbriggs444

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?