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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model for flexible stick

I'm trying to model a flexible stick with a partial differential equation. I want one of the ends to be fixed and the other end to swing. Do you guys know of any good models I can use? Any ...
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199 views

Why is it easier to glide on sharp ice skates than on dull skates?

There have been previous questions (e.g. here and here) on Physics.SE about the mechanism that makes ice skating possible. Reviewing these, as well external references, it seems pretty clear that the ...
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1answer
82 views

Mathematically impossible for a vortex line to have loose ends?

Could someone show the math behind it? Source : "A vortex is a bunch of air circulating around itself. The axis around which the air is rotating is called a vortex line. It is mathematically ...
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94 views

Why does air circulate on an airfoil — The Kutta Condition [duplicate]

Why does the air circulate on a flowing airfoil, thus giving rise to increased velocity (circulation + relative airspeed) above the wing and hence decreased pressure.
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201 views

Why friction force is force of constraint?

My understanding about constraint force is that it is a force which limits the geometry of particle's motion. For example, situations such as the particle trapped in a track or limited in domain can ...
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50 views

Applied / environmental question: direction of exhaust fumes

I'm not sure the Physics StackExchange is the perfect place for this environmental/applied physics question, but as I found no forum more fitting I ask my question here. Otherwise please move my ...
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2answers
264 views

Shouldn't the Uncertainty Principle be intuitively obvious, at least when talking about the position and momentum of an object?

Please forgive me if I'm wrong, as I have no formal physics training (apart from some in high school and personal reading), but there's something about Heisenberg's Uncertainty Principle that strikes ...
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2answers
91 views

How does isotropy of free space imply $L(v^2)$ for a free particle? [duplicate]

From Mechanics; Landau and Lifshitz, it's stated on page 5: Since space is isotropic, the Lagrangian must also be indpendent of the direction of $ \mathbf{v}$, and is therfore a function only of ...
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1answer
144 views

Spring Damper System for a Vibrating Motor

Good day people of SE I have a friend that has a final year project and is stuck. He has a motor with a small weight at the end of the shaft that causes vibrations. This motor is on a thin plate. ...
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103 views

2d pool collision with rotational motion

I'm trying to calculate two 2d disks' collision with rotational motion. The collision is perfectly elastic: the sum of translational and rotational energy is conserved. In the instant of the collision ...
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1answer
89 views

Find Angular Momentum about any point

How do I find the angular momentum of a body about any point? We know that $L=I\omega$ for a body rotating in space, where $L$ denotes the angular momentum, $I$ denotes the moment of inertia and ...
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2answers
607 views

Find the minimum value of velocity [closed]

Find the minimum value of the initial velocity $u$ of the particle such that the particle crosses the wheel of radius $R$. Details and assumptions $R=2m$ $g=9.8m/s^2$ Neglect air resistance. All ...
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99 views

Reasons to consider the coefficient of restitution velocity independent - conditions when this does apply

In high-school mathematics textbooks a bouncing ball is often considered as an example of an exponential decay. One can easily derive this if one assumes that the coefficient of restitution is ...
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6answers
2k views

Are there forces which do not involve a change in momentum?

I am familiar with the equation $$\vec{F}=m \vec{a}$$ I am wondering as to whether it is possible for something to exert a force on another object without changing the momentum of said object. My ...
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3answers
341 views

Strain energy density in index notation

The strain energy density is defined as $$dU = \int_0^{\epsilon_{ij}} \sigma_{ij} d \epsilon_{ij}$$ (see Reddy "Energy Principles and Variational Methods in Applied Mechanics", 2nd Ed, 4.11). Assuming ...
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1answer
122 views

Time inversion for Euler equation in fluid dynamics

Consider Euler equation for continuum body: $$\frac{\partial u^i}{\partial t}+\mathbf u\cdot \nabla u^i=- \frac{1}{\rho} \frac{\partial p}{\partial x^i} $$ where $\rho$ is the mass density, $p$ is ...
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176 views

Does limit $\hbar \rightarrow 0$ in Quantum Mechanics mean anything?

Assuming that I learn Quantum Mechanics first, and then I approach Classical Mechanics as a special case of Quantum Mechanics, I will definitely find the relationship between Quantum Mechanics and ...
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1answer
144 views

Equation of a flying kite

My question is the following: What is the shape of the rope which holds a kite flying? (Steady state.) I am not a physicist (I am a mathematician), so I can not work the physics part of the ...
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118 views

Correct way to include constant external force in virial and pressure calculation

Halo, given a simulation cell with N particles where particles interact only with bond and pair potentials and periodic boundary conditions (minimum image convention) are used. On a subgroup of ...
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1answer
73 views

Two masses collide on a ramp [closed]

M1 slides down a frictionless ramp and collides with M2 They both compress the spring. How far is the spring compressed? What is the final velocity of M1 on the rebound up the ramp? I was thinking ...
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1answer
4k views

How to calculate the moment of inertia of a solid cube

How do I calculate the moment of inertia of a uniform solid cube about an axis passing through its center of mass? I also wanted to know if the moment of inertia ...
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2answers
143 views

Angle rotated by a rod when it's hit by a pendulum

Consider a pendulum of length $h$ with a bob of mass $m$ it is held horizontally at and angle of $90^{\circ}$ with the vertical. A rod of mass $M$ and length $h$ is pivoted at its upper end and this ...
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2answers
78 views

Homework Question involving Momentum [closed]

I'm trying to solve a homework problem as review for an exam I have tomorrow and I was wondering if someone could help explain it to me. It is as follows: You are at Lowe’s shopping for bricks ...
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1answer
441 views

Modeling a 2-dimensional mass spring system

First of all, I am unfortunately not an expert in physics, so please be indulge with me. I am trying to model a $2$-dimensional mass-spring system with $1$ mass and $3$ springs to solve a dynamics ...
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1answer
83 views

$\cos^{2}(\phi)$ in the kinetic energy term of the Lagrangian is one?

I'm doing some homework in Classical Mechanics, and is about to write out the Lagrangian of a system. But, when I check the answer from my teacher, something is missing. The kinetic energy I'm using ...
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1answer
150 views

From Lagrangian to equations of motion [closed]

I have a given Lagrangian: $$L= e^{st}\cdot\frac12\cdot(mv_y^2-ky^2)$$ And are asked to identify the equations of motions, the constants of motions and physical system. Without the exp-time-term, ...
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3answers
308 views

A particle of mass $m$ moves with constant speed $v$ along the curve $y^{2}=4a(a-x)$ [closed]

I have complications to do the following problem: A particle of mass $m$ moves with constant speed $v$ along the curve $y^{2}=4a(a-x)$. Find its velocity and acceleration vectors. My first idea was ...
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1answer
423 views

Pendulum with a rotating point of support from Landau-Lifschitz

I found this problem in Landau-Lifschitz vol.1 (Mechanics) A simple pendulum of mass $m$, length $l$ whose point of support moves uniformly on a vertical circle with constant frequency $\gamma$. ...
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2answers
280 views

Conservation of phase space volume in Rindler space-time

Let us consider Rindler space-time, i.e. Minkowski space-time as seen by a constantly accelerating observer. My question is, does Liouville's theorem, i.e. the conservation of phase space volume in ...
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0answers
80 views

Impulse & Momentum

please could someone check this MIT video (http://www.youtube.com/watch?v=Lkuo6nZ6nZM) at 26mins 31secs. He says that if you threw a tomato on a bathroom scale then you would get a certain force ...
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1answer
130 views

Lagrangian formalism and Contact Bundles

In his Applied Differential Geometry book, William Burke says the following after telling that the action should be the integral of a function $L$: A line integral makes geometric sense only if ...
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61 views

Good Source to Understand Angular Momentum [duplicate]

I am looking for a good source to understand angular momentum. I know the basics but I am looking for a sound in-depth knowledge like directions of angular momentum, when it is not parallel to angular ...
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1answer
76 views

Power and speed [closed]

I'm asked to calculate how much POWER a 1210kg car needs to drive with a 85 km/s speed up a 655 meter long slope of 4.5°. I can find how much energy and work is required to do this, but isn't ...
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71 views

Bullet energy loss in solid materials [closed]

Does someone know simple model of energy loss in solid materials for a solid bullet? For example: I want to estimate momentum transferred to a thin plastic plate given by a small bullet. No matter ...
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1answer
113 views

Classical disintegration of particles, Landau-Lifshitz series on Physics

i read Landau's book recently. In this book p.43 Landau says from (16.1) (16.2) can be write down $T_10$= $p_0^2$/2$m_1$=($M-m_1$)($E_i-E_1i-E_i'$)/$M$ For me, it is hard to understand the factor ...
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1answer
139 views

Moment of inertia of a system in different cases

A rod of mass $m$ and length $l$ is pivoted at one end to ceiling and free to rotate in the vertical plane. A disc of radius $R$, which is less than $l$, can be fixed at its other end in 2 ways : ...
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1answer
320 views

Why does a car bonnet (hood) rise when you connect the clutch with a brake on?

Is the rotational force to overcome the brakes moved to the opposite effect of moving the car chassis, until the brake is released?
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3answers
808 views

Do we need inertial frames in Lagrangian mechanics?

Do Euler-Lagrange equations hold only for inertial systems? If yes, where is the point in the variational derivation from Hamilton's principle where we made that restriction? My question arose ...
6
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2answers
380 views

Why is classical mechanics determinism based on position and momentum only and not forces and scattering rules?

Consider a closed system (say a box) of $n$ particles. There is a well-known idiom/meme/law in classical mechanics that says that the position and momentum of those $n$ particles is all that is needed ...
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1answer
217 views

Why isn't $F = \frac{\partial \mathcal{L}}{\partial q}$?

If momentum is, $$p = \frac{\partial \mathcal{L}}{\partial \dot{q}}$$ and force is, $$ F = \frac{dp}{dt}$$ and by Euler-Langrange equations, $$ \frac{d}{dt}\frac{\partial \mathcal{L}}{\partial ...
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1answer
108 views

Conceptual question on superposition of forces holding a specific mass in equilibrium

Consider a point mass $x$ (like for example the earth in space) and let $A$ and $B$ be two sets of point masses which each hold the point mass $x$ in equilibrium, meaning the acceleration induced by ...
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1answer
65 views

The superposition of force (or acceleration) configurations

My question is quite specific as it refers to this article but I hope that someone here could help me. I cite the relevant part of the article: ... The second example consists of gravitational ...
6
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1answer
274 views

Why don't clouds fall? [duplicate]

Well I do know that they sometimes fall as rain, but my question is why don't the droplets fall as soon as they condense from steam to cloud. Clouds are white by the process of Mie scattering so the ...
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2answers
254 views

Tangential acceleration in circular motion?

A lot of my problems have objects moving in circular paths with tangential and normal components of acceleration. If the tangential component is non-zero though, the speed is changing so the radius ...
2
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3answers
1k views

Where is the energy lost in a spring?

Thinking about springs, and their extensions, I recently came to a confusion which I hope this wonderful community can help me solve. The question is this. When the block is initially attached to ...
2
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0answers
101 views

Stress calculations in a perforated paper

You have a sheet of paper (torn out of a good quality foolscap notebook) as shown above, and you start pulling it apart with both your hands (forces indicating by the blue arrows). Its difficult to ...
2
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1answer
266 views

Push a box in a plane with friction. How to deal with the rotation?

Suppose I have a box (say, length-1m, width-1m, height-0.5m) on the plane with friction. I can apply a horizontal force in on the surface of the box. If the force doesn't pass through the center of ...
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1answer
77 views

Kinetic energy and temperature

I've randomly been thinking about smoothies and internal energy all weekend. If we have an assortment of fruit in the solid phase and then proceed to blend it all so that it ends up being in the ...
5
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1answer
164 views

How Hamilton's Principle was found?

Hamilton's principle states that the actual path a particle follows from points $p_1$ and $p_2$ in the configuration space between times $t_1$ and $t_2$ is such that the integral $$S = ...
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1answer
116 views

What is the neatest way to describe a “non-autonomous” (lagrangian) system?

The configuration space of a system of particles $(m_i,x_i)$, $i=1,\dots,n$, subject to constraints $$\Phi (x)=0,\qquad \Phi\colon \mathbb R^{3n}\to \mathbb R ^{3n-k},\qquad x=(x_1,...,x_n),$$ if the ...