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 $-i\hbar\vec\nabla$ for momentum in quantum mechanics, while $m\vec{v}$ in classical mechanics?

I am a little bit confused when thinking of the momentum representation in QM and CM. In QM, momentum is represented as $-i\hbar\vec\nabla$, while in classical, momentum is represented as $m\vec{v}$. ...
0
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2answers
69 views

Taking time derivative of two dependant variables

I'm not entirely sure if this is correct. I have to take the time derivative of the following: $$\frac{d}{dt}mr^{2}\dot{\phi}$$ Now, both $r$ and $\dot{\phi}$ depends on the time $t$, so I have to ...
10
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1answer
583 views

Are the Hamiltonian and Lagrangian always convex functions?

The Hamiltonian and Lagrangian are related by a Legendre transform: $$ H(\mathbf{q}, \mathbf{p}, t) = \sum_i \dot q_i p_i - \mathcal{L}(\mathbf{q}, \mathbf{\dot q}, t). $$ For this to be a Legendre ...
-1
votes
1answer
149 views

Can someone explain the solution (provided) of this conical pendulum work problem [closed]

In the image, it looks like the tangential direction is always 45 degrees away from the string, not 90 degrees. Is it not the circular path that the solution is talking about?
9
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3answers
5k views

Why does water gulp out of a water bottle with a narrow opening instead of a steady flow?

For example, take a water bottle. Fill it with water and then turn it upside down. Instead of flowing steadily downward, it gulps down in parts. Why?
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2answers
135 views

How do I properly write Newton's second law for a particle with drag?

A heavy particle is projected at speed $U$ at an angle $\alpha$ to the horizontal. The particle is subject to air resistance which is experimentally found to vary proportionally to the square of ...
1
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0answers
90 views

stopping, moving of mobile phone when vibrating

A mobile phone move aside when it vibrates. How is that happening ? and most importantly is it possible to make any changes to the vibration motor to stop moving when vibrating or any other methods to ...
0
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2answers
121 views

If a paper disc is cut into a spiral, does its moment of inertia change?

It is obvious that there is no change in the mass of it and its radius. But the shape of the object does change. Does it mean its moment of inertia will also change?
2
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1answer
141 views

Casimir Invariants of the Galilean group

I had studied a couple of things about Galilean and Poincare group. But in the Galilean group, there is not enough clarity on how to calculate generators for boosts ($B_i$), which if I do it seems I ...
2
votes
2answers
377 views

How can I tell that circular motion is a solution for a particle confined to the surface of a cone?

I'm working on a problem where a particle of mass $m$ is confined to the surface of an inverted half cone (and is circling downwards due to gravity), with the cone's half angle $\alpha$. I chose to ...
1
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5answers
140 views

Why is the independence of orthogonal vector-quantities always implicit in books/lectures?

The "theorem" that I can "just" separately deal with orthogonal quantities (like horizontal and vertical force or velocity, etc), I never found explicitly mentioned, but just implicitly in the ...
0
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0answers
33 views

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 ...
6
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2answers
639 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 ...
3
votes
1answer
97 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 ...
0
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0answers
95 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.
0
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0answers
633 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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0answers
85 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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votes
7answers
710 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
133 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
208 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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0answers
133 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 ...
7
votes
2answers
1k 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 ...
2
votes
0answers
166 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
514 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 ...
6
votes
1answer
146 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 ...
4
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1answer
466 views

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

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 ...
0
votes
1answer
212 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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0answers
161 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 ...
0
votes
1answer
95 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 ...
1
vote
3answers
10k 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 ...
0
votes
2answers
207 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
107 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 ...
1
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1answer
831 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 ...
1
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1answer
92 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 ...
1
vote
1answer
223 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, ...
3
votes
3answers
385 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 ...
5
votes
1answer
900 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 $\gamma$. ...
11
votes
2answers
319 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 ...
1
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0answers
113 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 ...
8
votes
1answer
151 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 ...
0
votes
0answers
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 ...
0
votes
1answer
82 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 ...
1
vote
0answers
86 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 ...
0
votes
1answer
157 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
259 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
485 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?
9
votes
3answers
1k 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
votes
2answers
631 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 ...
6
votes
1answer
231 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 ...