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.