What is the relationship between kinetic energy and angular momentum?

• 5 Replies
• 3084 Views

0 Members and 1 Guest are viewing this topic.

jeffreyH

• Global Moderator
• Neilep Level Member
• 4175
• The graviton sucks
What is the relationship between kinetic energy and angular momentum?
« on: 21/12/2014 16:05:27 »
The kinetic energy I am interested in is that involved in forward motion through space. What is the relationship between these two motions?
Fixation on the Einstein papers is a good definition of OCD.

alancalverd

• Global Moderator
• Neilep Level Member
• 4895
• life is too short to drink instant coffee
Re: What is the relationship between kinetic energy and angular momentum?
« Reply #1 on: 21/12/2014 17:03:03 »
They are both conserved. So when rigid gravitational masses move past each other, they will follow curved paths such that the total angular momentum and kinetic energy remain constant.
helping to stem the tide of ignorance

jeffreyH

• Global Moderator
• Neilep Level Member
• 4175
• The graviton sucks
Re: What is the relationship between kinetic energy and angular momentum?
« Reply #2 on: 21/12/2014 17:42:47 »
They are both conserved. So when rigid gravitational masses move past each other, they will follow curved paths such that the total angular momentum and kinetic energy remain constant.

Thanks Alan.  I need to do a bit more reading up on this but just wanted an initial response to confirm my initial thoughts.
Fixation on the Einstein papers is a good definition of OCD.

PmbPhy

• Neilep Level Member
• 2804
Re: What is the relationship between kinetic energy and angular momentum?
« Reply #3 on: 21/12/2014 20:46:09 »
Quote from: jeffreyH
What is the relationship between kinetic energy and angular momentum?
Jeff. Have you studied Lagrangian or Hamiltonian mechanics as of yet? If so then you'd have known the answer to this question. That's the benefit of studying various forms of mechanics.

You want a relationship between K and p, right?

p = mv

$$\frac{p^2}{2m} = \frac{(p)^2}{2m} = \frac{(mv)^2}{2m} = \frac{m^2v^2}{2m} = \frac{1}{2}mv^2 = K$$

Q.E.D. $$K = \frac{p^2}{2m}$$

jeffreyH

• Global Moderator
• Neilep Level Member
• 4175
• The graviton sucks
Re: What is the relationship between kinetic energy and angular momentum?
« Reply #4 on: 21/12/2014 21:28:13 »
Quote from: jeffreyH
What is the relationship between kinetic energy and angular momentum?
Jeff. Have you studied Lagrangian or Hamiltonian mechanics as of yet? If so then you'd have known the answer to this question. That's the benefit of studying various forms of mechanics.

You want a relationship between K and p, right?

p = mv

$$\frac{p^2}{2m} = \frac{(p)^2}{2m} = \frac{(mv)^2}{2m} = \frac{m^2v^2}{2m} = \frac{1}{2}mv^2 = K$$

Q.E.D. $$K = \frac{p^2}{2m}$$

I have studied neither yet but I need to get round to that. Thanks for the equations they will be useful. Do you have any recommendations for textbooks on the above mentioned mechanics?
« Last Edit: 21/12/2014 21:29:51 by jeffreyH »
Fixation on the Einstein papers is a good definition of OCD.

PmbPhy

• Neilep Level Member
• 2804
Re: What is the relationship between kinetic energy and angular momentum?
« Reply #5 on: 21/12/2014 21:57:58 »
Quote from: jeffreyH
I have studied neither yet but I need to get round to that. Thanks for the equations they will be useful. Do you have any recommendations for textbooks on the above mentioned mechanics?
I'm happy to see that those relationship were what you had in mind!

The textbooks below are all very good and can be downloaded from the internet at the URLs I gave below the title for free. I'm sure you'll enjoy them. As always, I'm at your disposal.

The term Analytical Mechanics refers to the mechanics of Lagrangian and Hamiltonian Mechanics. See: http://en.wikipedia.org/wiki/Analytical_mechanics
One typically uses Variational principles in working with these areas of classical mechanics.

The Variational Principles of Mechanics by Cornelius Lanczos (1970) is famous for this branch of mechanics. It's quite well-known.

Newtonian Mechanics by A.P. French  (1971) [Does not contain Analytical Mechanics]
http://bookzz.org/book/2033048/f8d850

An Introduction to Mechanics by Daniel Kleppner & Robert J. Kolenkow (1973) [Does not contain Analytical Mechanics]
(Not available online)

Classical Mechanics by John R. Taylor (2005)
http://bookzz.org/book/911552/c4bf66

Classical Dynamics of Particles and Systems by Marion and Thornton (2004)
http://bookzz.org/book/556792/ca7948

Solved Problems in Classical Mechanics; Analytical and numerical solutions with comments by O.L De Lange & J. Pierrus (2010)

Classical Mechanics by Haret C. Rosu
http://arxiv.org/abs/physics/9909035
« Last Edit: 22/12/2014 05:45:11 by PmbPhy »