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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What is the mathematical formulation for buckling?

Argument: Buckling is an engineering concept that can only be applied to thin columns with compressive loading. (Is it possible to) Prove the above sentence right or wrong with mathematical ...
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0answers
159 views

Conveyor scales modeling

Assume we have a conveyor scales. Which consists of scales, and motor with conveyor belt placed above, so that the boxes can be measured (weight) while moving above. What I want is to create the model ...
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4answers
6k views

Torque vs Moment

I was wondering, why in Newtonian physics torque is called "torque" while in static mechanics they call it "moment"? I prefer by far the term "torque", for not only it sounds strong, but also ...
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1answer
2k views

Why are infinitesimal rotations commutative, whereas finite rotations are not?

Infinitesimal rotations commute and every finite rotation is the composition of infinitesimal rotations which should logically mean they also commute; but they don't. Why?
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3answers
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Force as gradient of scalar potential energy

My text book reads If a particle is acted upon by the forces which are conservative; that is, if the forces are derivable from a scalar potential energy function in manner $ F=-\nabla V $. I ...
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0answers
261 views

Flattening rate of a parabola

If you have a piece of paper that is furled and unfurled so that it's in the shape of part of a parabola, and knowing that if you leave it, it'll flatten itself after time, would it flatten faster if ...
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1answer
2k views

Is the static gauge pressure of a free jet always atmospheric?

Let's say I have a free jet of air leaving a pipe into the atmosphere. I know that the static gauge pressure at the pipe exit is equal to the atmospheric. But what about the static gauge pressure 10 ...
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1answer
200 views

What does this infinitesimal Eulerian change describe?

This is a question I originally posted in math.se which received an answer that was far too mathematically sophisticated for what I wanted; given that basic multivariable calculus was used through out ...
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1answer
267 views

Is the pressure at the outer hole on a pitot static tube equal to atmospheric pressure?

I'm looking at a pitot static tube question right now and I just need some clarification. There is the outer hole on the pitot static tube, not the hole that the air stream goes through, but the other ...
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0answers
147 views

How do I determine where the maximum air velocity around an object is?

I have a freestream of air directed at an object. Is there a way to find where the maximum air velcoty occurs with only having initial air speed and static pressure at the object?
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4answers
891 views

Why does a ping pong ball change direction when I spin it on a table?

When I spin a ping pong ball on the table, it rolls forward in the opposite direction of the spin, and then eventually changes direction and rolls backward. Here's a video demonstrating the effect. ...
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1answer
446 views

D-brane Lagrangian?

As I understand it from the threads I read, D-branes are viewed as somewhat secondary to strings: If I know what all the open strings do, then I know what the D-branes do as well. But if the D-brane ...
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1answer
891 views

Question Concerning Dimensional Analysis

In the first lecture of MIT's Classical Mechanics Professor Lewin talks about Dimensional Analysis.He talks about an apple being dropped from a certain height can be quantitatively expressed as the ...
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1answer
253 views

Is there a Newton's third law for the em field?

There is a momentum associated with the em field that ensures the conservation of total momentum for a system of interacting charges. Can the same be done in an analagous way to ensure Newton's ...
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1answer
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What phrases describe collisions with coefficients of restitution less than zero or greater than one?

The coefficient of restitution describes the elasticity of a collision: 1 = perfectly elastic, kinetic energy is conserved 0 = perfectly inelastic, the objects move at the same speed post impact ...
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1answer
76 views

How must you spin the ball to make it alternate between 2 positions? [closed]

Assume any parameters you may need. Thanks in advance.
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2answers
15k views

Difference between momentum and kinetic energy

From a mathematical point of view it seems to be clear what's the difference between momentum and $mv$ and kinetic energy $\frac{1}{2} m v^2$. Now my problem is the following: Suppose you want to ...
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0answers
431 views

Classical mechanics: Generating function of lagrangian submanifold

I have a short question regarding the geometrical interpretation of the Hamilton-Jacobi-equation. One has the geometric version of $H \circ dS = E$ as an lagrangian submanifold $L=im(dS)$, which is ...
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7answers
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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 ...
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2answers
470 views

Kinetic energy puzzle

System S1 moves at constant speed V with respect to S0 in one dimension: ...
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4answers
448 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 ...
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2answers
756 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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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 ...
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1answer
179 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 ...
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1answer
96 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
450 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
184 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
400 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
269 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 ...
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0answers
611 views

Physics tension question [closed]

Two blocks are pulled across a frictionless surface by a $240\ N$ force, as shown in the diagram below: $60\ kg$ - - - cord - - - $20\ kg$ → $240\ N$. If the blocks are accelerating at $3\ m/s^2$ what ...
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0answers
111 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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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
votes
2answers
378 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 ...
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votes
2answers
4k 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
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1answer
576 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
2k 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 ...
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1answer
257 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
393 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
508 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 ...
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2answers
801 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?
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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
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1answer
147 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
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1answer
858 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
256 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
777 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 ...
3
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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 ...
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2answers
302 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
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2answers
875 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 ...
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2answers
864 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 ...
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4answers
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“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, ...