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    Question about derivation of Euler-Lagrange eq.

    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...
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    Why doesn't time get slower and slower in a g-field?

    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...
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    Free fall down (Chord) Tunnel through Earth

    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...
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    Conceptual question about force/torque on a rigid object

    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...
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    What if Newton's laws were shifted by one time derivative?

    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)
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    Best next step for tackling quantum 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...
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    Deriving motion of a displaced piston on a gas cylinder

    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...
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    USAPhO 2014 F=ma exam #14, (rotational dynamics)

    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...
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    Physics C Mechanics: torque on a yoyo

    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...
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    Quick Calc Correction

    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...
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    USAPhO 2014 F=ma exam #19, (tension, static equilibrium)

    Unfortunately there's no link to the test. This is from the test administered a month ago. Homework Statement 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. Which of...
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    Wind in a rotating space settlement?

    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...
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    USAPhO 2011 F=ma exam #12, (gravitational force, 3 body)

    http://www.aapt.org/physicsteam/2012/upload/exam1-2011-1-3-answers_1.pdf Homework Statement 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...
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    USAPhO 2009 F=mA exam #25, (torque, rotational energy)

    http://www.aapt.org/physicsteam/2010/upload/2009_F-maSolutions.pdf Homework Statement 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...
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    USAPhO 2009 F=MA exam #16, (angular frequency of a spring)

    http://www.aapt.org/physicsteam/2010/upload/2009_F-maSolutions.pdf Homework Statement 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...
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    USAPhO 2008 F=ma exam #18, (gravitational potential)

    http://www.aapt.org/Programs/contest...08_fnet_ma.pdf [Broken] Homework Statement 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 ring’s gravity...
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    USAPhO 2009 F=MA exam #13, (spring SHM)

    Homework Statement 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...
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    USAPhO F=ma 2010 exam # 17 (Gravitational potential energy)

    Homework Statement Four masses m are arranged at the vertices of a tetrahedron of side length a. What is the gravitational potential energy of this arrangement? Homework Equations U = -Gm2 / r The Attempt at a Solution The potential energy is the negative of the work done by gravity in...
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