So "the first order variation in S (action) has to be zero for S to be at a minimum" is just a fancy way of saying "the derivative of S is zero at a minimum"?
"Just as the ordinary derivative of a function has to be zero at the function's minimum, so to does the action have to be unchanged by small variations in the path near the minimum of the action."
Okay, please explain this analogy. I agree that the derivative of a function is zero at a minimum...
I've attached the part from Landau & Lifschitz Mechanics where I got confused.
"The necessary condition for S(action) to have a minimum (extremum) is that these terms (called the first variation, or simply the variation, of the integral) should be zero. "
Why is this a necessary condition? If...
g-field as in gravitational field (character limit)
As far as I know, special relativity says that observers traveling fast experience slower time than observers at rest. So if an observer were to accelerate in a space ship, his time would get slower and slower relative to ours.
But the...
I caught my mistake. It's in the "Solving for r" stage. I foolishly assume d is an arc instead of a flat chord.
Admins, please feel free to delete this thread. Not sure how to.
Homework Statement
I'm trying to show that any tunnel through the Earth (not necessarily through the center) will have a free-fall time that is the same. I heard this was true somewhere.
Homework Equations
acceleration of free-fall = GM / r^2 where r is changing
I believe this involves...
@DaleSpam, thank you for the prompt help. Now that I think about it, I suppose angular momentum would be different between points because L is not a property of the object, it is a property of each reference point.
KE, I thought, is a property of a system when viewed from a certain reference...
I've taken up to the equivalent of first year undergrad mechanics, but this simple concept is unclear to me.
Say a force F is applied (perpendicular) to a rod (in a vacuum with no gravity-- F is the only external force) at a non center of mass point A for a tiny time dt. How does it move...
Thank you, @haruspex.
4) Yup, equal and opposite-- oops.
3) I have some questions about angular momentum. I understand it's only meaningful if you choose an axis. Say you choose the axis of Cylinder 1. Then L = Iω. But how does the spin of Cylinder 2 add into the total angular momentum about...
@logan3 Kinetic energy is not conserved because this is not an elastic collision. This site explains it well, I think:
http://hyperphysics.phy-astr.gsu.edu/hbase/elacol.html
When two objects in a collision stick together, you can be sure it's an inelastic collision, not an elastic collision...
So, just to clarify, in problems like this, where two spinning cylinders rub together and bring each other to rest:
1) Energies aren't equal, so one cylinder's energy can't be equated with the other's
2) Momenta aren't equal (?), so the cylinders' momenta can't be equated.
3) Neither energy...
What would be some important properties of a universe where Force = Mass * Jerk and objects stay in constant acceleration until acted upon by a net force? (if we ignore the fact that objects would reach the speed of light, and just deal with classical mechanics)
Doesn't the energy-time version of Heisenberg's Uncertainty Principle say that mass/energy can pop into existence for very short times?
Might be a silly question, but this is what I've gathered from reading about it.
By optics I hope you mean an in depth study of light, deriving the wave equation from Maxwell's equations, etc. Not the mirrors and lenses crap that we have to suffer in high school.
Okay, but what happened to " a force on an object is a force on an object" (paraphrased from somewhere above)?
I understand why it would rotate. I picture the inertia of the object to be a force that points opposite in direction to the external force.... But given a free body diagram, how...
Yeah- I thought it would get messy. I saw a thread on here that asked "if a book is pushed across a surface, why does it stop rotating and translating at the same time" and I was mind-boggled.
It seems that calculating the frictional force at any time would take a messy integral... and...
Got it guys, thanks. I have another question that will help me a lot. I think it's related, so I won't start a new thread.
If an object, say a book, is on a frictionless surface and experiences a force AT ANY point, not necessarily the CM, it will accelerate with no rotation, correct...
Could someone please answer the following question to help me understand free-body diagrams better?
If an object (say a yoyo) has a force mg acting downward at its CM, AND a force T = mg from the string that I'm pulling acting upward at it's edge, what motion will it exhibit? Technically, the...
Wow, never heard of Lagrangian and Hamiltonian before your post. Thanks for leading me to the Susskind lectures. I think what you were talking about was a 9 lecture series in classical mechanics (found it on iTunes). Does the course involve math beyond easy MV calc?
Also, you're right, I...
To be completely, immaturely honest, *points at Einstein* I wanna do what he's doing.
Modern physics. The stuff you see on Fabric of the Cosmos and shows like that. Maybe when I choose to specialize in a specific field, I'll have to learn some condensed matter physics or something, but for now...
Can't tell if that's sarcastic haha.
The curriculum hasn't changed. I think it's pretty shallow-- no respectable university should place students based on scores from this exam.
Also, it sounds like you took AP Physics C two years ago? Do you have any suggestions for me, especially...
Okay, well now I'm doubting whether rushing into modern physics is a good idea.
If I'm interested in a career in pure physics, should I spend more time right now reinforcing my foundation? I don't know what the Lagrangian and Hamiltonian formulations of classical mechanics are. I wikipedia'd...
I'm a high school student who has completed classical mechanics and electrodynamics with calculus (equiv. AP Physics C).
I'm interested in learning quantum mechanics as soon as I can. I've heard of kids my age who are learning that stuff already. Then I open a textbook and see crazy stuff...
First, I'm a second year high school physics student so my thinking may be half-baked. I was wondering what motion a piston would exhibit if it was the frictionless lid of an ideal gas cylinder with a constant amount of air, and if it was pushed or pulled a little bit.
There would be a...
Uh, this might not be the right place, but I have a question for all of you PhysicsForums veterans with thousands and thousands of posts. I've just been incredibly impressed by the level of discussion here and I want to get where you are.
What are you educations? What did you focus on in...
PDF: http://www.aapt.org/physicsteam/2014/upload/exam1-2014-2-2-answers.pdf
Homework Statement
A disk of moment of inertia I, mass M, and radius R has a cord wrapped around it tightly as
shown in the diagram. The disk is free to slide on its side as shown in the top down view. A
constant...
If you want, the problem is here: q.s 23-24 in http://teachers.sduhsd.net/jdanssaert/AP%20Physics%20C/AP%20Physics%20C%20review%20material/AP%20C%20MC%20test%20mech%202009.pdf
Homework Statement
A solid cylinder of mass m and radius R has a string wound around it (basically a yoyo). A...
I'm brushing up on calculus. I don't see how this derivative works.
x(t) = A cos(ωt - \varphi)
v(t) = dx / dt = - Aωsin(ωt + \varphi)
I get that the derivative of cosx is -sinx. I get that the omega is brought outside the cos function because of U substitution.
Why does the the...