# Question about energy in C-O-M frame and Lab frame.

Hi, I just register to this site.
I'm reading a famous classical mechanics textbook. and it state that
'Since the spatial momentum in the C-O-m frame is zero, there is clearly more energy, p0, in this frame than in the laboratory frame.'

I think the energy in the center of momentum(C-O-M) frame should be less than in all other frame.
However, I've still not sure that it's right or wrong because this textbook is very famous.

Thanks.
PS. Should I states the name of the text?

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tiny-tim
Homework Helper
welcome to pf!

hi sukho! welcome to pf!

that certainly looks wrong, but i wonder what the context is

Bill_K
sukho, you are correct, it should be less. It's a well-known theorem in mechanics that the kinetic energy of a system of particles can be written as a sum of two terms: T = ½ MV2 + ∑ ½ mivi2, where M is the total mass, V is the velocity of the center of mass, and vi are the velocities of the individual particles with respect to the center of mass. Clearly this is a minimum when V = 0.

Bill_K
Oops, just noticed this is the relativity group. Ok, even easier. The total 4-momentum of the system of particles is P = (E/c, p). This has norm P·P = (E/c)2 - p.p. Since the norm must be the same in all reference frames, E will be minimum in the center of mass frame where p = 0.

Meir Achuz
Homework Helper
Gold Member
It would help, if you can give the exact reference, to see the context of that quote.
The book could be talking about available COM energy, which is larger in a colliding beam accelerator.

Meir Achuz
Homework Helper
Gold Member
It would help, if you can give the exact reference, to see the context of that quote.
The book could be talking about available COM energy, which is larger in a colliding beam accelerator.

Hi, everyone.
The book I read is 'Classical Mechanics' 3ed by 'Goldstein Poole & Safko' on page 302 line 16
and if u see the footnote on this page, it's kind of support the context. I also confuse about the footnote too.
Thanks.

tiny-tim
Homework Helper
hi sukho!

i don't think that's available online …

can you post a picture?

Hi. I attached pdf file of the context.
The attached file is a page 302, Goldstein. and the context is on line 16.
Thanks.

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• 292.6 KB Views: 120
tiny-tim
Homework Helper
hmm … it refers to equations (7.79) and (7.80) which are on the previous page

Meir Achuz
Homework Helper
Gold Member
Hi. I attached pdf file of the context.
The attached file is a page 302, Goldstein. and the context is on line 16.
Thanks.
Reading it in context, it does not make too much sense. I am not sure what their p^0 refers to.
Maybe just ignore that sentence.

Last edited by a moderator:
Reading it in context, I see (as I thought) that G is referring to the sum of the energies of the two particles. Since E^2-p^2 is invariant, this is largest when p-0.

Why it's not minimum energy when p=0, as Bill_K said? it's minus sign before p^2.
and the I've attached the previous pages.
Thanks.

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• 766.4 KB Views: 138
I think I'll just ignore that context.
Thank you guys.