Classical mechanics refers to the classical (i.e., non-relativistic, non-quantum) study of physics. Three major formulations of classical mechanics are newtonian mechanics, lagrangian mechanics, and hamiltonian mechanics. The latter two are rather useful in extensions to Classical Mechanics; ...

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Rubber Band Forces

I have a question regarding the force a band places on an object. Say I have a rubber band wrapped around 2 pegs at a certain distance, and at that distance I know the pounds of force per inch it is ...
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298 views

Why $\frac{d}{dt}r_{a}\nabla_{a}U_{ab}+\frac{d}{dt}r_{b}\nabla_{b}U_{ba}=\frac{d}{dt}U_{ab}?$

In classical mechanics for two mass particles $a$,$b$ we assume the symmetric potential arising from $F_{ab}$ and $F_{ab}$ given by $$U_{ab}(r)=-\int^{r}_{r_{0}}F_{ab}(r')dr'$$ and ...
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166 views

Say we're driving a bike and suddenly hold the brakes?

It's easy for me to imagine that if we brake the front wheel then there is a chance that I'll flip. On the other hand if I brake the back wheel, there is no way it'll happen no matter how fast I ...
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Has any permanent magnet motor been proven to run?

I have read lots of articles about permanent magnet motors, some of which claim the possibility and other which refute it. Is it possible to have a permanent magnet motor that runs on the magnetic ...
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391 views

Numerical torque calculation

Suppose I can compute interaction energy of two rigid bodies as a function of their coordinates of centers of masses and Euler rotation angles (total 6 + 6 degrees of freedom). Now I can numerically ...
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180 views

Linking two balls together

I have a physics simulator that simulates a bunch of balls moving and colliding with each other, and I would like to be able to "link" two balls together so they stick to each other (are always ...
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Why do we need the quantity momentum?

Why do we need the quantity Momentum in physics when we have the quantities like Force and Energy? Isn't it possible to substitute the usage of Momentum with equivalent of Force and Energy?
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1answer
664 views

How does a star wobble due to orbiting bodies

What equations determine how a star wobbles in response to an orbiting planet, and can it be used to determine the mass of distant objects based on the wobble? If there are other more reliable ...
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Conservation of angular momentum in helicopter

I have a small RC-controlled toy helicopter with removable tail rotor. Suppose I remove the tail rotor, hold the tail with my hand, start the rotor until it moves with constant angular velocity and ...
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382 views

How to determine n equidistant vectors from point P in three dimensions

As an assignment for uni I need to figure out an algorithm that explodes a particle of mass $m$, velocity $v$, into $n$ pieces. For the first part of the assignment, the particle has mass $m$, ...
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Difference b/w Kinetics & Kinematics w/concrete example

(I know whether I understand this or not doesn't matter much to my work & study but am just curious.) I still can't differentiate in my head kinetics and kinematics (similar thread is found but ...
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Can a force in an explicitly time dependent classical system be conservative?

If I consider equations of motion derived from the pinciple of least action for an explicilty time dependend Lagrangian $$\delta S[L[q(\text{t}),q'(\text{t}),{\bf t}]]=0,$$ under what ...
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446 views

Will a precessing spinning wheel fall down if there is no friction at all?

If there where no friction at all, would a spinning wheel held up by one end of the axis spin precess forever without falling down? I just asked another question about the same problem: Direction ...
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Direction of torque precession of a spinning wheel

Consider a spinning wheel, which is held up by one end of it's axis like this: To explain why the change of angular momentum is directed as shown in the figure above, one usually says that there is ...
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How to interpret this vertical circular motion problem?

A bucket of water is tied to a rope and swung in a vertical circle. The distance from the bucket centre to the axis of rotation is $2.08m$. Calculate the angular velocity (in $rad s^{-1}$) of ...
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520 views

What techniques can be used to analyze a rod rotating about the edge of a table?

A uniform rod of length $4x$ is rotating about the edge $O$ of the table. (The rod does not fall off the table.) The centre of mass $G$ of the rod is distance $x$ away from $O$. The rod is making ...
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Normal force in a compound pendulum (physical pundulum) system?

Consider a compound pendulum pivoted about a fixed horizontal axis, illustrated by the force diagram on the right: # Okay, I can't figure out where the normal force on the pendlum should point ...
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Calculate relativistic boost to COM frame from two arbitary velocities?

Looking in Goldstein's book, there doesn't seem to be a standard formula to calculate the COM frame velocity for two particles, from their relativistic velocities in the lab frame, although it is done ...
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651 views

What sustains a rigid body's rotation at its constant angular(rotational) speed?

Continuing from the following scenario from my previous question Centripetal force of a rotating rigid body? : Consider someone pushing a roundabout in a playground. Initially the roundabout is ...
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Why aren't stratospheric balloons compressing their helium to descent? [closed]

I can't find a reference of a working stratospheric balloon mounted with a compressor to control its altitude. Is there a big physical difficulty (such as compressor weight/power ratio, or power ...
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365 views

moment of tennis racket & volley

I've been looking for the relation between moment of a tennis racket and its maneuverability. If I define maneuverability as the easiness to get in position for quick reaction strokes like volleys and ...
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2answers
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Would this model of a boat move according to Newtons 3rd Law?

If i have a small toy boat with a sail, and i attach a fan onto it, FACING THE SAIL, which runs by solar. Once the fan turns on will the boat move or will it remain at rest. Apparently it wont because ...
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111 views

understanding the oscillating part of the Gutzwiller trace

given the density of states according to Gutzwiller's trace formula $ g(E)= g_{smooth}(E)+ g_{osc}(E) $ i know that the 'smooth' part comes from $ g_{smooth}(E)= \iint dxdp \delta(E-p^{2}-V(x)) $ ...
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What is the exact definition of center of gravity?

I've come across many definitions. Is it 1) The point from which the weight of the body acts, i.e., the point at which if the entire mass of the body is assumed to be concentrated, the gravitational ...
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Why do non-Newtonian fluids go hard when having a sudden force exerted on them?

You can dip your hands into a bowl of non-Newtonian fluid but if you are to punch it, it goes hard all of a sudden and is more like a solid than anything else. What is it about a non-Newtonian fluid ...
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352 views

How do I visualize the non-coaxial rotation of this device?

The picture below shows an isolated system with a fairly massive wheel at one end, attached via its axle to a long shaft, like a bike tire on a bike frame, but the bike frame is merely a low mass ...
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267 views

two pendulums, which pendulum has shorter period [duplicate]

Possible Duplicate: A pendulum clock problem There are two pendulums. First pendulum consists of a rod of length L and flat heavy disk of radius R (R < L), disk is connected rigidly to ...
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930 views

Can relativistic kinetic energy be derived from Newtonian kinetic energy?

Relativistic kinetic energy is usually derived by assuming a scalar quantity is conserved in an elastic collision thought experiment, and deriving the expression for this quantity. To me, it looks ...
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138 views

sending information over a wire--mechanically [duplicate]

Possible Duplicate: Is it possible for information to be transmitted faster than light? I've thought about this since I was a little kid. I know it isn't exactly feasible, but it still ...
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1answer
516 views

Maximum speed of a water skier

Water skiing is a sport where an individual is pulled behind a boat or a cable ski installation on a body of water, skimming the surface. Consider an idealized case where the boat is moving at a ...
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172 views

Functional determinant approximation

Let the Hamiltonian in one dimension be $H+z$, then I would like to evaluate $\det(H+z)$. I have thought that if I know the function $Z(t) = \sum_{n>0}\exp(-tE_{n})$ I can use $$\sum_{n} ...
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2answers
983 views

Is the change in kinetic energy of a particle frame independent?

Intuitively, I would expect the change in kinetic energy of a particle to be frame independent. It just doesn't "feel" right that between two points in time-space, one frame should measure a change in ...
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595 views

The form of Lagrangian for a free particle

I've just registred here, and I'm very glad that finally I have found such a place for questions. I have small question about Classical Mechanics, Lagrangian of a free particle. I just read Deriving ...
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109 views

Orbits for space missions

I am just wondering say if there is an expedition where some astronauts are sent to the moon, how do they choose the trajectory for the spaceshuttle (or whatnot)? I mean there are many possible ...
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308 views

A question regarding particle trajectories in the symplectic manifold formalism

How to solve a free particle on a 2-sphere using symplectic manifold formalism of classical mechanics ? Is there a way to get coriolis effect directly, without going into Newton mechanics? And is ...
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1answer
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Classical Mechanics for Mathematician [duplicate]

Possible Duplicate: Which Mechanics book is the best for beginner in math major? I am looking for suitable ways to learn mechanics in mathematician's perspective. I went through: ...
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Deriving the Lagrangian for a free particle

I'm a newbie in physics. Sorry, if the following questions are dumb. I began reading "Mechanics" by Landau and Lifshitz recently and hit a few roadblocks right away. Proving that a free particle ...
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650 views

A Question about Virtual Work related to Newton's Third Law

In describing D'Alembert's principle, the lecture note I was provided with states that the total force $\mathbb F_l$ acting on a particle can be taken as, $$\mathbb F_l=F_l+\sum_mf_{ml}+C_l,$$ ...
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187 views

Does locality emerge from (classical) Lagrangian mechanics?

Consider a (classical) system of several interacting particles. Can it be shown that, if the Lagrangian of such a system is Lorenz invariant, there cannot be any space-like influences between the ...
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When “unphysical” solutions are not actually unphysical

When solving problems in physics, one often finds, and ignores, "unphysical" solutions. For example, when solving for the velocity and time taken to fall a distance h (from rest) under earth gravity: ...
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How do levers amplify forces?

This is really bothering me for a long time, because the math is easy to do, but it's still unintuitive for me. I understand the "law of the lever" and I can do the math and use the torques, or ...
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123 views

Is there analysis library for stress-strain data?

I have three column data that has time-displacement-force from 1D tensile/compression test. Now I would like to get the standard mechanical properties of the material, like Young modulus, yield ...
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2answers
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Can these figures demonstrating the safety of “Archery Tag” arrows be correct?

There is a new sport called "Archery Tag" that involves shooting opponents with foam-tipped arrows fired out of a real bow. The official Archery Tag web site presents data that claims to show the ...
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4answers
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Finding Lagrangian of a Spring Pendulum

I'm trying to understand Morin's example of a spring pendulum. What I don't get is his expression for $T$. I can understand the $\dot x^2$ term in the brackets. But I don't understand the $(l + ...
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2answers
341 views

Hamilton's equations in terms of initial conditions

I'm trying to understand the way that Hamilton's equations have been written in this paper. It looks very similar to the usual vector/matrix form of Hamilton's equations, but there is a difference. ...
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4answers
574 views

Is the quantization of the harmonic oscillator unique?

To put it a little better: Is there more than one quantum system, which ends up in the classical harmonic oscillator in the classial limit? I'm specifically, but not only, interested in an ...
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146 views

Interacting classical strings?

May classical strings be interacting? I would guess no, I can not see any way to break a classical closed string in two of them (the "pants" diagram); but maybe I'm missing something.
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Piston movements in four stroke cycle?

I was reading about a four stroke cycle. Here's what I understood: In the first stroke, the piston starts at the top and moves down. In the second stroke, the piston moves upwards. In the third ...
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Factors affecting torque and RPM of a motor

I am not a physics guy, so not even the basic concept of a DC motor is easy for me. My question is as follows: How do these parts of a motor affect its RPM and Torque? I had my research a while ago ...
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Shape of rotating rope (lasso problem?)

Let's take a wire or a rope. I usually do this with a chain or my scarf. I fixate one end in my hand and apply rotation (by subtle movements of this endpoint like spinning a lasso). The rope gets ...