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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“Principle of least action” and “Principle of conservation of energy”: Which one is fundamental and which one is derived? [closed]

Suppose I throw a ball upwards. First it will rise under gravity and then fall under gravity. During the rising part the kinetic energy gradually decreases and the potential energy increases until ...
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44 views

Force as a Function of Position

If given a velocity as a function of position, is force as a function of position just it's derivative times the mass? I'm given the following and I am not sure my above logic is correct: The speed ...
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0answers
16 views

Equality of external derivatives in Canonical Transformation implies invariance of Poisson Brackets

For a canonical transformation, we require that the forms $$p'dq'- H'dt$$ and $$pdq -Hdt$$ differ up to a total differential. From this follows the equality of the external derivatives: $$\sum_i ...
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3answers
62 views

How simultaneous information of coordinates and velocities sufficient to completely determine the subsequent motion of a mechanical system?

I somehow could not find the answers to the question in Why are coordinates and velocities sufficient to completely determine the state and determine the subsequent motion of a mechanical system? to ...
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76 views

Why is a sphere easier to move than a box of the same mass?

Is it only because of the less friction involved or at there other reasons?
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122 views

How is the Poisson bracket $\{\mathbf{c},\mathbf{l}\cdot\hat{n}\}=(\hat{n}\times \mathbf{c})$, for constant $\mathbf{c}$, and not zero?

The Poissonian formulation of mechanics tells us that for a generating function $g(q,p,t)$, the Poisson bracket of some function/variable $f(q,p,t)$ with the generating function corresponds with an ...
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53 views

Rigid body motion degrees of freedom

A rigid body moving in $\mathbb{R^2}$ has 3 degrees of freedom and in $\mathbb{R^3}$ has 6 degrees of freedom. Could you please help me show that a rigid body moving in $\mathbb{R^n}$ has ...
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2answers
97 views

Proof that 1d lattice displacement by phonons is given $u_{n\pm 1}(t) = A_ke^{i\omega_k t} e^{i knd}e^{\pm i k d}$

I looked in «Kittel - Introduction to solid state physics», Wikipedia and Google for the derivation that: A phonon of wavenumber $k$ displaces the $s$-th atom in a monoatomic 1d crystal lattice by a ...
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Im learning Work-energy theorem, this question popped into my mind about Force applied and displacement

I know a lot but I'm not sure, I'm guessing if $400J$ of work done on a 800 Newton object, if I'm correct, $400N$ to $800N$..that is $.5 m$ displacement, so by $W=∆KE$ why do I get $200J$? I was ...
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3answers
76 views

Magnitude of Normal Force in Circular Motion

In the above diagram an object is in vertical circular motion. At $T_0$ the object is at pos1, and at that position, I have shown the forces resolved. So $F_n-mg\cos(a)$ is the centripetal force ...
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53 views

Statistical Physics of a System with Friction inside a Hot Bath

If you have a classical system (i.e obeying Newton's equations of motion) with Hamiltonian $H(x,p) = \frac{p^2}{2m} + U(x)$ then the statistical behaviour of this system is described by the ...
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Friction in Lagrangian Method [duplicate]

A uniform, flexible chain of length $l$, mass $m$, hangs off a frictionless table-top of height greater than $l$. The length of the part of rope hanging off is $x$. Gravity accelerates the part of the ...
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66 views

Long and short barreled guns

Projectiles containing delicate elecrtronic equipment may be damaged if they are subjected to high accelerations. For this reason, such projectiles may be fired from guns with long barrels but not ...
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21 views

Relative velocity of the center of mass in a rotating coordinate system

Say I have a rigid body in space. Let k be a stationary coordinate system, K a coordinate system rotating together with the rigid body, so the transformation $B:k \rightarrow K$ it's just a simple ...
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0answers
46 views

Rolling Resistance Coefficient

I found that rolling resistance can be expressed with this equation: $$F_\mathrm{rr} = \frac{C_\mathrm{rr} W}{r}$$ Where $C_\mathrm{rr} =$ coefficient of rolling resistance $W =$ normalforce $r ...
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2answers
60 views

Can a system be designed that uses no energy to accelerate particles to high velocity?

I have one system in mind. Although I know it is not possible to accelerate a particle to a higher speed without spending energy, I would like to know why the proposed system won't work. The system ...
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1answer
40 views

Confusion with Thomas precession

Suppose an inertial frame $S^\prime$ is moving with a relative velocity $\textbf{v}=v\hat{n}$ w.r.t another intertial frame S with their axes parallel and $\hat{n}$ is an arbitrary direction. In that ...
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1answer
28 views

A Classical/Theoretical problem regarding Friction

I had a rod. I broke it into two. Now I wish to make it one i.e. to join those (not glue or any thing as such) as if the rod was not broken at all. This is our objective! As I broke the rod apart, ...
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123 views

Work and forces in systems of many particles

I'm reading Goldstein's Classical Mechanics, first chapter, and am confused about what's going on in equations of forces and work in systems of particles. For example, Goldstein calculates work done ...
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1answer
77 views

Gravitational potential energy lost by an object falling on the earth [closed]

I am stuck on this simple question: g is the strength of the gravitational field at the surface of the Earth; R is the radius of the Earth. Show an equation describing the potential energy ...
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2answers
44 views

How do you tell whether a force acting on an inclined plane is going up or down in its perpendicular component to the plane?

I'm practicing mechanics, and I had to resolve the following forces perpendicularly to the inclined plane in order to work out the reaction force (plus the weight of the ball) But I cannot tell ...
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1answer
37 views

How to scale variables in a classical Hamiltonian?

So I looked at some research articles where one has a classical Hamiltonian $H(p,q,t) = p^{2}/2 + V(q,t)$. If one introduces the scaling transformation $$t \mapsto t/\sqrt{s}, \quad H \mapsto Hs, ...
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1answer
34 views

Why are the integrability conditions necessary and sufficient for the existence of a canonical transformation's generating function?

Consider a canonical transformation $(p,q) \rightarrow (P,Q)$ under a generating function $F$. The condition for form invariance of Hamiltonian equations of motion looks like : $$\sum_{s}P_s\dot{Q_s} ...
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33 views

car dashboard problem

I stumbled upon this question while I was driving my car. On my dashboard I have fuel gauge and engine temperature gauge next to each other, look at the pic: http://i.stack.imgur.com/aDgKj.png Fuel ...
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1answer
66 views

How did he find the “lambda” value in this question? [closed]

There is a pdf i found when searching about Lagrangian Multpliers, but i was not able to understand how he derived lambda from two differential equations. If anyone can walk me through it, i would be ...
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36 views

Maximizing horizontal displacement from projectile motion off of downward slope [closed]

Firstly, I think I should point out that I am a high school student, so please excuse me if my question seems mediocre. What I am doing was seemingly simple, I am doing some research on projectile ...
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2answers
19 views

How to determine the friction constants

We know that the friction is formulated in this form $$F=av+bv^2+Nμ$$ I'm working with an object and surface and I want to find $ a, b, μ $ for them. Can you please give me an experimental method ?
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Origin of spin and direction in the magnus effect

If you solve the Bernoulli equation: $$p=p_0-\rho_0{v^2 \over 2}$$ using a complex flow potential for a flow around a cylinder: $$W(z)=v_0 z + {v_0 R^2 \over z} - {\Gamma \over 2 \pi } \ln(z)$$ you ...
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1answer
29 views

Phase Portraits Given Hamiltonian

Given a Hamiltonian say $$ H = 5p^2 $$ What is the correct procedure for producing a phase portrait. My initial thoughts were to solve the system of equations $\frac{dq}{dt} = 0$ and $\frac{dp}{dt} ...
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0answers
16 views

Impulse response of coupled oscillators

The behaviour of a LTI system can be described entirely by it's impulse response. Imagine the following coupled pendulums have no friction losses. They will have 2 resonant frequencies, one for when ...
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28 views

Classical Quantum or Relativistic? [closed]

An ensemble contains free electrons at 10^3 electrons per m^3 at 10^7 K. What can this ensemble be treated as: a Classical Quantum or Relativistic gas or in some overlapping domain?
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41 views

Energy method to solving equations of motion? Why does this method work and what is it called?

Given the stated system in the photo we are suppose to prove simple harmonic motion when given an initial displacement $x$ I first considered the total energy of the system which we will call $H$ ...
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Equivalent spring constant of setup

A mass $M$ is suspended using two springs having spring constant $k_{1}$ & $k_{2}$ with distance from mass as $a$ & $b$ respectively. Find equivalent spring constant of system. So I ...
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1answer
35 views

Can point mass have vibrational motion?

Can a point mass have vibrational motion. I have read that reason for point mass is to ensure that we can idealize translational motion and don't have to worry about rotational and vibrational motion. ...
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1answer
27 views

Diagonal of a thin rectangular foil, inertial principal axis?

I'd like to know if the diagonal of a thin foil is an inertial principal axis. I know that if an axis isn't a symmetry axis then it isn't a principal axis. In the rectangle the diagonal isn't a ...
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9answers
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Why is it possible to drive a nail into a piece of wood with a hammer, but it is not possible to push a nail in by hand?

It is possible to drive a nail into a piece of wood with a hammer, but it is not possible to push a nail in by hand. Why is this so?
3
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1answer
59 views

1kg mass impacting at half light speed - effects?

Such a mass would have kinetic energy approximating a 1 mega-tonne thermonuclear weapon. So, what would such an object do if it hit the Earth? We know how destructive such an energy release can be, ...
3
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0answers
42 views

Elastic collision / relative velocity problem [closed]

I'm having some trouble with a homework exercise and I'd really appreciate some help! I've done the first part correctly (according to the solution sheet), but I can't seem to get the second part ...
3
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4answers
95 views

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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30 views

Find the angle of the projectile [closed]

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 ...
3
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2answers
133 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 ...
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2answers
101 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 ...
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46 views

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

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 ?
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68 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 ...
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3answers
70 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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3answers
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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 ...
2
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4answers
162 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 ...
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1answer
33 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 ...
3
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2answers
92 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 ...