# Kinetic energy of a sphere

1. Apr 22, 2015

### Quarlep

Lets think we have a sphere and it moves a constant veloctity v.So it will have a kinetic energy.Is this kinetic energy efectts spheres particle energy.(sphere made up but atoms)

Thanks

2. Apr 22, 2015

### Drakkith

Staff Emeritus
Sure, the sum of the kinetic energy of each atom equals the total kinetic energy of the sphere.

3. Apr 22, 2015

### nasu

Not in the common definition. The KE of a macroscopic object does not include the internal KE. Not that you cannot think about it this way, too.

4. Apr 22, 2015

### Drakkith

Staff Emeritus
Hmm, I suppose that the KE of the atoms would be part of its temperature then?

5. Apr 23, 2015

### Quarlep

Lets think another way we have a object uniform density then this object moves.then the kinetic energy will be sum of the small mass of the sphere.then we get it whats wrong in this model

6. Apr 23, 2015

### Staff: Mentor

Can you rephrase your question. I'm not sure what you are asking.

7. Apr 23, 2015

### Quarlep

Lets suppose we have a sphere.Sphere has a uniform density.When v=0 the total energy of sphere will be U(lets describe it that way).Now If we move the object with speed v then total energy will be U+1/2Mv2.Now we can divide M small m's like M=m1+m2... so then total energy will described that way.Like 1/2m1v2+1/2m2v2...=1/2Mv2.Important think is uniform density.Whats wrong in this model ?

8. Apr 23, 2015

### Staff: Mentor

I don't see anything wrong with that model. (We are ignoring any molecular structure and internal energy, just treating it as a classical continuum.)

Why do you think it's wrong?

9. Apr 23, 2015

### Quarlep

I am not telling wrong but nasu says its not correct.So I am confused.

10. Apr 23, 2015

### Staff: Mentor

nasu was just pointing out that that would ignore the random thermal motion of the molecules. Which is often done.

If all you are interested in is the macroscopic mechanical energy (such as gravitational PE and macro KE), then you can safely ignore the details of internal energy.

11. Apr 23, 2015

### Quarlep

Thank you

12. Apr 23, 2015

### sophiecentaur

You can't add up the particle KE to get the bulk KE but you can add up all the momentums.

13. Apr 23, 2015

### Staff: Mentor

But if you treat the object as classical rigid body, ignoring any molecular-level structure and internal energy, you can divide it into pieces and add the KE of each piece to get the total macroscopic KE of the object.

14. Apr 23, 2015

### sophiecentaur

Well, it would give you an answer but what could you do with number you got? I can't think it would give you a measure of how much energy you might extract from the system, for instance. (Except, perhaps, for a hot cannonball hitting a bucket of water and producing loads of hot, fast moving droplets of water. ?)

15. Apr 23, 2015

### nasu

Yes, if you divide it into pieces, all moving with the same velocity, the total KE is the sum of the KE of the pieces. But this is quite trivial.
These pieces are not the atoms or molecules, as hinted in the OP.

My understanding was that he asks how the macroscopic motion influences the KE of atoms. But I am not sure.

16. Apr 23, 2015

### Staff: Mentor

It might be trivial, but it is essential to understand. And it doesn't just work for pure translation, where every piece has the same velocity (that would be quite trivial).

I'm not sure what he's asking.

17. Apr 23, 2015

### Quarlep

A sphere moves a constant velocity.This sphere has a volume.Each per volume in the sphere has a mass and If we calculate all this mass kinetic energy we get total kinetic energy of object. Post 7 If object type change thinks I want you to focus galaxy.Lets consider galaxy is a sphere and stars are atoms so galaxy total energy can be the sum of stars kinetic energy.Galaxy has a uniform density.

18. Apr 23, 2015

### Staff: Mentor

Sure. I assume you mean that you subdivide the sphere into pieces and calculate the kinetic energy of each piece and add them up. That will give you the total KE.

19. Apr 23, 2015

### Quarlep

Yeah I mean exactly that. Can somebody tell me last decision of it ?

20. Apr 23, 2015

### Staff: Mentor

What do you mean?