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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Intuitive explanation of $1/2(at^2)$ motion equation?

The full equation $$ Xf = X_o + V_o t + \frac{at^2}{2} $$ is integrated from the velocity function (which was integrated from constant acceleration function), right? The problem is, I can't seem to ...
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0answers
95 views

To prove uniqueness of a rotation tensor for general rotation of a rigid body

Suppose there are $N$ particles embedded in a rigid body which undergoes some random rotation such that: $$ \overline{\overline {R}}_{ij} \otimes \vec{a}_{ij} = \vec{b}_{ij}$$ where, $i$ and ...
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0answers
23 views

Find the angle of the projectile [on hold]

Given: Hmax = 2 * Range Find the angle of the projectile. After using the formula for both Hmax and Range, I got an angle of 74.69 if I am not mistaken. On the math exam teacher said the answer ...
1
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3answers
722 views

Why does weak equivalence principle say gravity is equivalent to acceleration?

I am told that the weak equivalent principle, that $m_i=m_g$ (inertial and gravitational masses are equivalent) is equivalent to the statement that in a small system you can't tell whether you are in ...
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3answers
186 views

Problem in Euler-Lagrange imply Newton

I'm self-studying Mechanics and I have a little problem: We can see that in Landau's book or in Wikipedia that when we inject the lagrangian in Euler Lagrange equation the term $\frac{\partial ...
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0answers
29 views

Showing the relationship between focal ratio and brightness [on hold]

I have an optics question that I have been stuck on for a few days now and I really need some guidance. Any help is appreciated! Question: The f-number (focal ratio) of a lens is the ratio of a focal ...
0
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1answer
233 views

Equivalency of conditions involving angular momentum of a rolling ball hitting a wall

(59th Polish Olympiad in Physics) A ball of mass $m$, radius $r$ and a moment of inertia $I = \frac 25 mr^2$ is rolling on the floor without sliding with the linear velocity $v_0$. It hit the wall ...
6
votes
2answers
251 views

Does a simple double pendulum have transients?

Suppose, we have the most simple double pendulum: Both masses are equal. Both limbs are equal. No friction. No driver. Arbitrary initial conditions (no restriction to low energies) Does this ...
0
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2answers
37 views

What is the difference between vortexing and centrifuging?

I understand that vortexing will result in mixing / re-suspension of particles, and that centrifugation will result in the separation of particles. However, what is the difference in the physics that ...
1
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1answer
56 views

How does the Moon influence atmospheric pressure?

I have just read in the Telegraph an article entitled Moon overhead makes rainfall lighter, scientists conclude. In that article there is the following statement: When the moon is overhead, its ...
13
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3answers
3k views

Why do we travel in a circle along the Earth?

I know that in order to travel in a circle I have to have a net centripetal force $F=mv^2/r$. I also know that my normal force and gravitational force cancel. How, then, am I traveling in a circle ...
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0answers
28 views

How does the gradient operator pick up a minus sign when the reference frame is switched from one particle to another? [on hold]

A potential between two particles, $i$ and $j$, is given as a function only of the separation distance, $$V_{ij} = V_{ij}(|r_i − r_j|)$$ It should follow that the force by $j$ on $i$ is equal and ...
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0answers
22 views

Why a wave, travelling in a lighter medium, inverts upon reflection from an interface of a denser medium? [duplicate]

As exactly the title says: Why a wave, traveling in a lighter medium, inverts upon reflection from an interface of a denser medium ? What are the things that go on at the interface ?
0
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1answer
41 views

Motion of Particle due to Lorentz Force

So my professor gave us the following question: A particle with electric charge $Q$ and mass $M$ is initially traveling with velocity $v_0$ in the $x$ direction at time $t= 0$. There is a constant ...
0
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3answers
43 views

Direction of velocity and acceleration for a pendulum [duplicate]

The image below shows the direction between acceleration and velocity change with time. But it seems to me that the direction is not opposite. Can you please see and tell if this is correct?
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2answers
2k views

How to model/simulate pressures and flows in a network of pipes

I'm having a hard time finding information on how to model/simulate this. I attached a couple files, both of which show an example tank & pump network. It's just nonsense that I made up for this ...
2
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4answers
150 views

Regarding the usage of 'classical potentials' in quantum mechanics

I am familiar with basic quantum mechanics and I know that there is no concept of 'force' in quantum mechanics, unlike in classical mechanics. Problems in quantum mechanics are solved by writing down ...
3
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2answers
76 views

Again, why is kinetic energy and velocity independent of position coordinates in Cartesian coordinates [duplicate]

This might be a very simple question. I read one previous post Can the kinetic energy be a function of the position vector? I know that in Cartesian coordinates, the kinetic energy ...
0
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1answer
11 views

Angular velocity when a rod inclined to a wall slips and its subsequent motion observed from the axis of rotation

When a rod inclined to a wall slips, rate of change of which angle does the angular velocity represent? Is it the rate of change of angle with which the rod is inclined to the horizontal ? I'm not ...
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1answer
43 views

Equivalent spring constant of an nth order system [on hold]

I am looking for the spring constant of this below diagram I think the solution will look something like this But I am looking for more like a generalized formula. Any help is appreciated. Also ...
0
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1answer
43 views

Why does quantum mechanics produce different predictions for Bell test experiments than classical mechanics?

I understand that experimental results from Bell test experiments have shown that measured correlation is a cosine function of the angle between the detectors. What I am struggling to grasp is why ...
0
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3answers
450 views

Advantages/Disadvantages of “hanging off” a motorcycle when leaning

The closest question I could find with regards to this subject was this one: Countersteering a motorcycle However, it does not address the specific physics of what I would like to know. There are 3 ...
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3answers
30 views

Effect of internal force on the weight of an object

A man is holding a closed cage on the palm of his hand with a bird in it. When the bird flies with an upward acceleration inside the cage, it feels heavier. But the force due to the bird in the cage ...
3
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3answers
101 views

What is the point of complex fields in classical field theory?

I see a lot of books/lectures about classical field theory making use of complex scalar fields. However why complex fields are used in the first place is often not really motivated. Sometimes one can ...
9
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3answers
896 views

Boundary layer theory in fluids learning resources

I'm trying to understand boundary layer theory in fluids. All I've found are dimensional arguments, order of magnitude arguments, etc... What I'm looking for is more mathematically sound arguments. ...
0
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1answer
126 views

Consistent method for finding direction of static friction

I am having trouble coming up with a consistent method of determining the direction of static friction. So far the best I have come up with is: it should oppose the relative acceleration the contact ...
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2answers
26 views

Balancing Utensils: Center of Mass

If you have a cork piece on top of a nail, it is extremely hard to keep it stable, and the slightest action will make the cork fall off. However, when you balance it on top of a nail but put forks ...
0
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1answer
40 views

Why does the energy of the mechanical wave depend on frequency but the EM wave does not?

Why does the energy of the mechanical wave depend on frequency but the EM wave does not? Are there any implications?
0
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1answer
208 views

Explanation of force amplification inside a solenoid

For a system being actuated by a motor, the force can be amplified by gearing. The energy is being used for force instead of distance, so it produces more torque but moves slower. For a system being ...
6
votes
2answers
301 views

Extending the ergodic theorem to non-equilibrium systems

I try to make this as short and concise as possible. For equilibrium systems in statistical mechanics, we have the Liouville's theorem which says that the volume in phase space is conserved when the ...
1
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1answer
79 views

How much force would it take for you stop the Moon from crashing into the earth once it has started to fall?

In my previous question, I asked how much force it would take to destabilize the Moon's orbit enough for the moon to start falling into the Earth and collide. Assume this has already happened. Now, ...
1
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1answer
26 views

How to calculate the pressure inside hose subjected to weight? (Example)

Example: Suppose we have a garden hose laid on a concrete floor. This garden hose is made out of rubber and is sealed on both sides. It is completely filled with water with no air bubbles whatsoever. ...
3
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3answers
44 views

If a bullet penetrates a bag, how come the repulsive force is constant?

I was doing a question on energy and forces, and it goes as follows:(Doesn't require knowledge of calculus): If a bullet with velocity $v$ penetrates a bag upto a distance $x$, then find the ...
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1answer
33 views

An impulse is given to a sphere out of the center?

I'm wondering what will happen if there is an impulse $J$ given to a sphere mass $M$ out of its center? I'm sure that it will rotate about the center, but what is its translational motion? It will ...
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2answers
42 views

Intuition behind Airy waves dispersion relation

Using Airy wave theory, one can derive the dispersion relation of water waves (under some physical assumptions): $$ \omega^2 = gk\tanh{kh} $$ where $k$ is the wave number, $h$ the distance from the ...
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0answers
19 views

Sensitive flame [closed]

As the year 1867 , Professor Tyndall explained the flame that is sensitive to sound ; The flame comes out from a pipe (it could be propane) and depends on some parameters like the flame speed $v_{f}$ ...
0
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1answer
35 views

Wind resistance [closed]

You have a metal plate/sign (max weight $5\, \text{kg}$) $1200\, \text{mm}$ long and $400\, \text{mm}$ high pivot/hinge at its base. A windspeed of $90 - 100\, \text{km/h}$ is applied to one face of ...
0
votes
1answer
257 views

What are the mathematical models for force, acceleration and velocity?

In mechanics, the space can be described as a Riemann manifold. Forces, then, can be defined as vector fields of this manifold. Accelerations are linear functions of forces, so they are covector ...
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0answers
26 views

How to calculate the torque of this example? [closed]

I was thinking a long time to solve this question .. I want to calculate the rope tension .. I want to use the torque to solve it .. What I managed to do is the following : $torque = ? - mg *cos(20) ...
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0answers
38 views

Higher order versions of momentum? Can conservation principles be established and used? [closed]

Question Can higher order derivatives of momentum be useful in creating theories of dynamics if they have conservation principles? Even if they aren't needed, could it be done in theory? For ...
2
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0answers
41 views

Kinetics of gas molecule [closed]

In the explanation of the nature of gases we use the kinetic formula $PV=1/3(mnc)$ where $p$ is pressure, $v$ volume, $m$ mass, $n$ number of molecules and $c$ means root mean square velocity. But in ...
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0answers
61 views

Clarification on conservation of energy for (or internal potential energy of) $N$ particle system

In Goldstein's Classical Mechanics, it says: Consider now the right-hand side of Eq. (1.29). In the special case that the external forces are derivable in terms of the gradient of a potential, the ...
2
votes
2answers
39 views

What orientation will let me drive the fastest with a tray of coffee on the floor? [closed]

I like coffee. I like to drive fast. These two don't usually go together, unless you like that coffee all over your floor because you tipped it over going around the corner. If I have up to four cups ...
1
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2answers
41 views

Motion of an object in a moving car and collison

I came across an interesting question today at work. 'Imagine traveling in a car. The passenger has a glass bottle in their hand. In which direction relative to the moving car should the passenger ...
4
votes
3answers
113 views

Can the kinetic energy be a function of the position vector?

,I got one confusion when reading Goldstein's Classical Mechanics (page 20, third edition). After getting the equation $$ \sum \left\{\left[\frac{\mathrm{d}}{\mathrm{d}t}{\left(\frac{\partial ...
15
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10answers
8k views

Book about classical mechanics

I am looking for a book about "advanced" classical mechanics. By advanced I mean a book considering directly Lagrangian and Hamiltonian formulation, and also providing a firm basis in the geometrical ...
3
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2answers
64 views

How can I use a magnet to lift a paperclip?

This question has been asked already, but no satisfying answer came up. All the answers seem to push the problem further, but do not explain clearly what is going on. I will reformulate it for a ...
0
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3answers
55 views

Measuring force of a punch

I'm trying to build a device that can mesure the force of a punch. ​ My initial plan was to build a platform with 4 springs (one at each corner) and an accelerometer in the middle. But, if the ...
4
votes
0answers
72 views

Second order Fermi mechanism. Is there a mistake in the Claus Grupen book?

The second order Fermi mechanism describes the interaction of charged particles with magnetic clouds. This model leads to a collision-less acceleration of cosmic rays up to ultra high energies. A ...
0
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1answer
37 views

Complex Coordinate change

I have a simple question where I must change the coordinates of a system however I am unsure whether I am correct. I am changing from Cartisian to complex coordinates. Let's say I only have $x$ and ...