What are inertia and noninertia frames

 Posts: 14
 Joined: Mon Dec 18, 2006 3:04 am
What are inertia and noninertia frames
Hi.
The study of kinematics and dynamics in noninertia frame is part of the GRE Physics test requirements.
Can someone tell me what are inertia and noninertia frames in the sense of mechanics?
Thanks.
The study of kinematics and dynamics in noninertia frame is part of the GRE Physics test requirements.
Can someone tell me what are inertia and noninertia frames in the sense of mechanics?
Thanks.

 Posts: 161
 Joined: Sat Nov 04, 2006 7:48 pm
I'll elaborate on CPT's response, just a bit. CPT was defining inertial frames, in a sense. The GRE's not going to test you on more than Newtonian mechanics in noninertial frames, and even that stuff will be at a fairly elementary level. A noninertial frame is a frame undergoing some sort of acceleration, be it rotational or translational. There are a whole lot of "pseudoforces" (as CPT put it) that account for an observer being "held" in that accelerating reference frame (ie centrifugal, corriolis, and transverse forces), and of course these forces would disappear as one converts back to an inertial frame. Sometimes they just make complicated problems easier to work out mathematically...but then again, if one's going for mathematical simplicity, why not just go all out and do your mechanics problems entirely in Lagrangian or Hamiltonian dynamics? It's a shame most undergrad curricula avoid the topic for so long...i think I was learning the QM Hamiltonian at least a semester or two before I was ever even introduced to classical Hamiltonian dynamics.
schmit.paul: While I more or less agree with you, I still think it's better to introduce the Lagrangian formulation only after you have developed sufficient intuition for working directly by looking at forces and being able to directly write down the equations of motion. The reason is that you can't really a Hamiltonian for every system (eg. dissipative systems), and while using the Lagrangian is helpful, it does help to have some idea of what each term in the equations of motion "is doing". This kind o intuiotion can only be developed over time, so I feel it's better that you spend some time doing things like this. Well anyway, that's just my tuppence.

 Posts: 161
 Joined: Sat Nov 04, 2006 7:48 pm
oh yeah, CPT, I agree that no physics curriculum should *start* with the Lagrangian formalism, but I think as soon as students have gotten to the point where they can solve basic partial differential equations in physics problems (ie, the point in the curriculum where the Schrodinger equation is introduced), the theoretical basis for working with a Hamiltonian should be given, and the classical context is the best way to approach this. At this point the student has probably already done just about everything there is to do in single particle classical mechanics, short of noninertial reference frames and complex multibody problems, so I make the assumption that the student at this point has a sufficient "intuition" with classical problems to not be confused sufficiently by an introduction to an alternative theoretical framework. Of course, that may not apply to everybody, but I would have liked to have seen it earlier and worked with it more extensively than just a few weeks at the end of a semester. For one, the prof. in my quantum III class had to derive the canonical momentum and the magnetic vector potential term in the Lagrangian in the classical context before he could discuss how to deal with magnetic fields in quantum, and I felt like that that should have been introduced to us the previous semester in our classical class. The sooner the better, within reason, just to get students more comfortable with it as early as possible. It's like learning a new language the younger people learn it, the easier it is to pick up and use fluently, before we've been too indoctrinated to solve problems a particular way.
Oh, definitely! I myself learnt the Hamiltonian formulation and Poisson brackets in the same semester that I learnt QM, which was good enough timing (so I assumed that you were advocating introducing Lagrangians even earlier, which I think is bit too much). Learning QM without familiarity with similar stuff in classical mechanics is a pretty skewed order of things, I'd say.
I took my first QM class before I had a formal introduction to Lagrangian and Hamiltonian dynamics. Most of us knew those thing were "out there" but didn't really have a good grasp of how they were came about or were used. Unfortunately my awful QM professor didn't do much to make it any better.
I definately thing QM and CM should go hand in hand. In fact, I think the best reason for learning CM in that abstract formalism is for comparison to QM. I mean, how can you understand you replace the momentum in the Hamiltonian with a momentum operator if you don't know what the Hamiltonian is in the first place?
I definately thing QM and CM should go hand in hand. In fact, I think the best reason for learning CM in that abstract formalism is for comparison to QM. I mean, how can you understand you replace the momentum in the Hamiltonian with a momentum operator if you don't know what the Hamiltonian is in the first place?
My point of view comes from my first QM class. Our crappy instructor tried to introduce path integrals to us, which of course involve the e^(action). Only the graduate students in the class had been exposed to action principle and the rest of us were lost. After an unenlightening semester of QM I decided to wait it out and take it with someone else. Now that I have CM and E&M under my belt I think I'll get much more out of it.