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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Why the Principle of Least Action?

I'll be generous and say it might be reasonable to assume that nature would tend to minimize, or maybe even maximize, the integral over time of $T-V$. Okay, fine. You write down the action ...
3
votes
2answers
483 views

Kinetic energy puzzle

System S1 moves at constant speed V with respect to S0 in one dimension: ...
0
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4answers
473 views

Whats wrong with this perpetual machine?

Consider a cube of mass M resting on a rough surface such that the coefficient of friction between the cube and the surface is K. So in order to just slide the cube I need to apply a minimum force of ...
3
votes
2answers
858 views

Relativistic effects

When are relativistic effects justifiably negligible? (I know that that is true for 'small velocities', but how small is 'small enough'?) 0.1c, 0.01c, etc.? And how does one properly justify that? I ...
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votes
3answers
1k views

Initial vs Constant Orbital Velocity

I am working on some basic physics simulation for a game and need to simulate gravity. I have a system working that is behaving more or less correctly so far, but I want to see if I can send a ...
0
votes
1answer
182 views

Is pressure distribution affected by shape

We have two iron (assume real-life stiffness) manhole covers resting on friction-less, perfectly smooth shims on flat ground. One is circular and the other square. If a force F is applied vertically ...
0
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1answer
98 views

Explain moving lightbulb [closed]

An acquaintance of mine, while being home alone, saw that the light bulb in the room which was hanging from the ceiling with wires having a pendulum motion which was more than noticeable. He says that ...
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2answers
506 views

How does the distance between two rails effect the speed of a steel ball bearing?

As part of a school science project, I constructed a Rollercoaster using Polyurethane tubing as rails for a steel ball bearing to rest on. In the process of building the coaster I observed that ...
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1answer
193 views

Extending Solutions To Hamilton's Equations to Whole Time Axis

In Arnold's Classical Mechanics book, he says "We assume that every solution to Hamilton's equations can be extended to the whole time axis", and adds that 'For this it is sufficient, for example, ...
3
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1answer
447 views

What variables does the action $S$ depend on?

Action is defined as, $$S ~=~ \int L(q, q', t) dt,$$ but my question is what variables does $S$ depend on? Is $S = S(q, t)$ or $S = S(q, q', t)$ where $q' := \frac{dq}{dt}$? In ...
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2answers
279 views

Why is it important that Hamilton's equations have the four symplectic properties and what do they mean?

The symplectic properties are: time invariance conservation of energy the element of phase space volume is invariant to coordinate transformations the volume the phase space element is invariant ...
2
votes
0answers
117 views

Surface normal on the earth to the sun at a given point in time

How complicated is it to calculate a surface normal on the spherical approximation of the earths surface pointing towards the sun at a given point in time? What I try do is to highlight a small area ...
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votes
1answer
1k views

How did Feynman derive the physics of medallion vs. plate wobble rate?

I am referring to this: Within a week I was in the cafeteria and some guy, fooling around, throws a plate in the air. As the plate went up in the air I saw it wobble, and I noticed the red ...
3
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2answers
399 views

Why does $\frac{\partial \mathbf{v}_i}{\partial \dot{q}_j} = \frac{\partial \mathbf{r}_i}{\partial q_j}$?

Why is the following equation true? $$\frac{\partial \mathbf{v}_i}{\partial \dot{q}_j} = \frac{\partial \mathbf{r}_i}{\partial q_j}$$ where $\mathbf{v}_i$ is velocity, $\mathbf{r}_i$ is the ...
2
votes
2answers
5k views

Normal force: up or down?

The normal force obviously always has direction perpendicular to the surface of contact, but I'm a bit confused about its sense: is it going 'up' or 'down'? I've seen articles on the web that describe ...
3
votes
1answer
600 views

Energy of a rotating disc around different moments of inertia

Lets take a disc that is rolling without slipping which has moment of inertia $I=kmR^2$. It will have total kinetic energy $E=\frac{1}{2}mv^2+\frac{1}{2}I\omega^2=\frac{1}{2}mv^2(1+k)$. Lets now use ...
3
votes
2answers
3k views

How do you calculate potential energy given a force that is dependent on time?

The restoring force of a spring is F(x) = -k(x-x0)exp(-t/T) where k and T are constants, x is the position of a mass on the spring, and x0 is the position of equilibrium of the spring. How do you ...
1
vote
1answer
320 views

Modellng mechanical behavior of heat shrink film

Consider a heat shrink film (as used in shrink sleeves that decorate plastic or glass bottles). These materials are produced by blow extrusion. When the film is heated (hot steam, hot air or ...
3
votes
2answers
421 views

How did L.H. Thomas derive his 1927 expressions for an electron with an axis?

I'm looking at the 1927 paper of Thomas, The Kinematics of an Electron with an Axis, where he shows that the instantaneous co-moving frame of an accelerating electron rotates and moves with some ...
6
votes
1answer
552 views

Circular motion when F=ma'

I apologize in advance if this question is deemed too general or too similar to this and this question. How would mechanics be different if $F=mx'''$ instead of $F=ma$? I feel like I have ...
10
votes
2answers
876 views

If the Earth didn't rotate, how would a Foucault pendulum work?

How does the Foucault pendulum work exactly, and would it work at all, if the Earth didn't rotate?
9
votes
5answers
5k views

Why Do Hurricane Balls Spin So Fast?

I was wondering if anyone could offer an explanation as to why the balls described in this video spin so fast. Here's the setup: Two metal balls are wielded together. When spun with air, they ...
2
votes
1answer
148 views

Confusion with the torque

Consider an imaginary vertical plane. Now say, a body is falling freely (under earth's attraction). If you consider any axis that is perpendicular to that plane. We get a non-zero value for torque. ...
2
votes
1answer
926 views

Lean angle of a turning bicycle

I'm asked to derive a relationship for the leaning angle of a bicycle with the following specs: Center of gravity for bike and rider is a distance $L$ above the ground when vertical, and the total ...
0
votes
2answers
261 views

Stress and strain

Let us consider a rod having a young's modulus $Y$. Let it be of length $l$, and suppose it is suspended from a point P. Let us pull the rod with a force $F$ at a point Q which is at a distance $2/3l$ ...
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2answers
828 views

kinetic energy and conservative force field

The kinetic energy of a particle is a periodic function in time. Does it imply that the particle is in a conservative force field and there are no dissipative forces acting on it at any instance of ...
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2answers
1k views

Integrals of Motion

Landau & Lifshitz write on the first page of chapter 2 of their Mechanics book (p.13) The number of independent integrals of motion for a closed mechanical system with $s$ degrees of freedom ...
2
votes
2answers
342 views

pressure exerted by fluid

If I had a flexible tube sealed at both ends and I submerged it in water (held vertical) Would the bottom half of the tube compress and the top half expand? What would the pressure in the tube be? Say ...
2
votes
2answers
981 views

Does the phase space (configuration and momentum space) of particles have a Euclidean norm? Does it have a useful meaning of “distance”?

Often in engineering physics, different vector spaces are used to visualize the trajectories (evolution) of systems. An example being the 6n dimensional phase space of n particles. It is not very ...
3
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2answers
981 views

Complete vs General Integral of first order PDE

The following is an excerpt from Landau's Course on Theoretical Physics Vol.1 Mechanics: ... we should recall the fact that every first-order partial differential equation has a solution depending ...
3
votes
4answers
2k views

“Regular” 20-sided die, vs “life counter” 20-sided die. Same probabilities?

Regular dice are made such that opposite sides of the die add to 1+the number of sides. For example, a 20-sided die has 14 and 7 opposite of each other, adding to 21. For certain types of games, ...
6
votes
2answers
927 views

What is the highest energy position for a double pendulum? And for which energy positions is it chaotic?

Math/physics teachers love to break out the double pendulum as an example of chaotic motion that is very sensitive to initial conditions. I have some questions about specific properties: For a ...
11
votes
1answer
214 views

Theorems on instability of classical systems of charged particles?

Classically, a hydrogen atom should not be stable, since it should radiate away all its energy. I remember hearing from my favorite freshman physics prof ca. 1983 about a general theorem to the effect ...
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3answers
829 views

Point particle moving on a frictionless semicircular hill

Consider an point particle moving on a frictionless semicircular hill (curve). The particle's initial kinetic energy is equal to the potential energy on the top of the hill, i.e it has the necessary ...
17
votes
1answer
1k views

Mechanics + Thermodynamics: Bouncing Ball

In preparation for an exam, I'm revisiting old exam questions. This one seems neat, but also quite complicated: A soccer ball with Radius $R=11cm$ is inflated at a pressure of $P =9 \times 10^4 ...
5
votes
2answers
356 views

Tracking photon color in Bell experiments

In parametric down-conversion, it is said that a driving photon is converted into two entangled photons whose frequencies add up to the driving frequency. Yet in discussions about entanglement ...
6
votes
2answers
321 views

Physical Interpretation of a Scalar Quantity Related to Currents/Conservation Laws

Let $Q_{ab} = (\psi_{;a})(\psi_{;b}) - (1/2)g_{ab}|\nabla \psi|^2$ be the energy-momentum tensor of the wave equation in some space time. I will use semicolons to refer to covariant differentiation ...
9
votes
3answers
637 views

How do we explain accelerated motion in Newtonian physics and in modern physics?

Maybe my question will seem stupid, but I am not a physicist so I have some problems understanding a classic Newtonian experiment: in the bucket experiment, why does he have to introduce the absolute ...
1
vote
1answer
3k views

How to calculate the exit velocity of a coil gun projectile?

First off, what quantities need to be factored in? Voltage and current through the coils, the magnetism of the projectile, the magnetic fields, etc.? Next, how would you calculate the speed of the ...
4
votes
1answer
181 views

Name of the guy that Feynman mentioned during a lecture: the diagram is of a chain hanging over a triangle

In a Feynman book, he talks about a man (I believe he lived 400-500 years ago) that discovered something about the dimensions of triangles (I think)by hanging a chain around the triangle. I've ...
1
vote
2answers
485 views

What method should I use to solve for the final acceleration of a projectile being launched from the earth's surface?

What method should I use to solve for the final acceleration of a projectile being launched from the earth's surface? The question I am working on is: A projectile is launched vertically from ...
6
votes
4answers
340 views

Maximal Gravity

I found this interesting problem in Introduction to Classical Mechanics with Problems and Solutions by David Morin: Given a point $P$ in space, and given a piece of malleable material of ...
5
votes
2answers
1k views

How is angular momentum conserved when a spinning top finally stops spinning?

Where does the top's angular momentum get transferred to? Does it very slightly change the angular momentum of the table, and then the angular momentum of the Earth?
11
votes
2answers
584 views

Essential background for QFT study

The preface to Mark Srednicki's "Quantum Field Theory" says that to be prepared for the book, one must recognize and understand the following equations: $$\frac{d\sigma}{d\Omega} = ...
31
votes
4answers
8k views

Why can't we feel the Earth turning?

The Earth turns with a very high velocity, around its own axis and around the Sun. So why can't we feel that it's turning, but we can still feel earthquake.
2
votes
1answer
232 views

Lagrange's equations: What is $\dot{q}_j$?

I'm looking at the solutions to a problem about a uniform thin disk. For the sake of this question, I start with $$L=\frac{1}{2}m\left( r\omega \right)^2$$ Then we plug it into Lagrange's equations: ...
3
votes
3answers
433 views

D'Alembert's Principle: Where does $-Q_j$ come from?

This is a follow-up question to D'Alembert's Principle and the term containing the reversed effective force. From the second term of Eq. (1.45) $$\begin{align*} \sum_i{\dot{\mathbf{p}}_i \cdot ...
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votes
1answer
810 views

D'Alembert's Principle and the term containing the reversed effective force

For our Classical Mechanics class, I'm reading Chapter 1 of Goldstein, et al. Now I come across Eq. (1.50). To put it in context: $$\begin{align*} \sum_i{\dot{\mathbf{p}_i} \cdot ...
3
votes
1answer
271 views

Coincidence detectors in Bell tests: How close is close enough?

When is a coincidence a coincidence? We know that to identify entangled photons, the electronics is set to look for simultaneous clicks at opposite detectors. The size of the window is to some degree ...
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2answers
264 views

Why isn't pressure used for flight?

Why isn't pressure used as flight? I've heard that 2L bottles can hold a pressure of up to 90 PSI safely. Since $F = PA$, if the nozzle of a pressure rocket is about 4 inches squared in area, that ...