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.
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.
acceleration of free-fall = GM / r^2 where r is changing
I believe this involves...
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...
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)
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...
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
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
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...
Unfortunately there's no link to the test. This is from the test administered a month ago.
A choppah is flying horizontally at constant speed. A perfectly flexible uniform cable is suspended beneath the choppah; air friction on the cable is NOT negligible.
Imagine a cylindrical space settlement. It spins about an axis to create pseudo gravity for residents, who will think that radially outward is "downward". The shape of this settlement is a toroid with a rectangular cross section.
Air is pumped in to make a habitable environment. Then...
You are given a large collection of identical heavy balls and lightweight rods. When two balls are placed at the ends of one rod and interact through their mutual gravitational attraction (as is...
Two discs are mounted on thin, lightweight rods oriented through their centers and normal to the discs.These axles are constrained to be vertical at all times, and the discs can pivot frictionlessly on...
Two identical objects of mass m are placed at either end of a spring of spring constant k and the whole system is placed on a horizontal frictionless surface. At what angular frequency ω does the system...
A uniform circular ring of radius R is ﬁxed in place. A particle is placed on the axis of the ring
at a distance much greater than R and allowed to fall towards the ring under the inﬂuence of the
Late correction, this is the 2008 F=ma exam: http://www.aapt.org/Programs/contests/upload/olympiad_2008_fnet_ma.pdf
A mass is attached to the wall by a spring of constant k. When the spring is at its natural length,
the mass is given a certain initial velocity, resulting in...
Four masses m are arranged at the vertices of a tetrahedron of side length a. What is the gravitational potential energy of this arrangement?
U = -Gm2 / r
The Attempt at a Solution
The potential energy is the negative of the work done by gravity in...