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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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. ...
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39 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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61 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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47 views

Finding Velocity and Displacement from Acceleration [closed]

First time posting, so please advise if and where I'm braking protocols. Here is the question I was given: A particle travels with acceleration given by $a(t)=(2e^{-t})i+(5\cos{t})j-(3\sin{t})k$. ...
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102 views

Randomness v. complexity

There are a few other topics I found that explore this idea from a different perspective: Is randomness deterministic? Can randomness exist? Is the universe fundamentally deterministic? My ...
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112 views

Differential holonomic constraints

Differential holonomic constraint is an integrable homogeneous first order differential equation: $$\sum_{i}\mathcal{E}_{i}(q)\frac{dq_{i}}{d\tau}=0;$$ in which $\sum_{i}\mathcal{E}_{i}(q)dq_{i}$ is ...
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50 views

When an object is moving at a constant velocity,would the normal force and $mg$ be equal?

Does the object's normal force and $mg$ cancel out, resulting in the two force becoming equal, or would one force be greater than the other? Thank you! Edit: Also would the $mg$ be considered weight ...
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74 views

hard sphere collision condition with periodic boundary conditions

Hello Stack Exchange Physics, I am curious if there is an analytical or efficient numerical solution for the collision of hard spheres in a rectangular unit cell with periodic boundary conditions. ...
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38 views

Determining Height of Platform on Fulcrum

Consider this scenario: We have a platform resting on a fulcrum. The platform's tilt is controlled by a motor attached to 2 levers: Is the link between the height of the top of the lever (...
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99 views

Force (torque) to break a bike handlebar? [closed]

Few weeks ago a neighbor manage to hit my bike with his car while the bike was parked next to a wall, check the picture. One side of the handlebar was at the wall and the door of his truck hit ...
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126 views

How does a cyclist moves the center of mass of the cycle-cyclist system?

Consider the image shown below, In the left diagram the centre of mass of the system lies upon the perpendicular from the point of contact. But in the right diagram the centre of mass has shifted ...
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114 views

Full time-derivative, Poisson brackets and Hamilton's equations (classical mechanics)

While studying Poisson brackets in classical mechanics and the derivation of $\dot{q_j}=\{q_j,H\}$ and $\dot{p_j}=\{p_j,H\}$ form of Hamilton's equations I encountered a surpsing identity, which led ...
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80 views

3D Dynamics: determining the moments of inertia on a plate with a couple

My Mechanical textbook (Bedford & Fowler 4th Edition) has a worked out example for determining a couple using euler's equations. This is not a homework question (at least I don't think it is?), ...
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169 views

Force of an object “skidding”?

Let's say I put the brakes on really suddenly in a car that was moving at 40mph. If I know how much force it takes to break the adhesion of the wheels, how do I find the force the car is exerting? ...
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180 views

What is the curve that describes the Daytime line in a Day and Night World Map?

A Day and Night World Map shows which parts of the Earth are in daylight and which are in night at a given instant. At one side of the Daytime line they are in daylight and at the other side they are ...
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39 views

When do I use center of mass versus conservation of momentum?

For example, if you are given your velocity in a problem where you are standing on a block slab which is on top of ice, you would use conservation of momentum. On the other hand, a question about a ...
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51 views

Is there a formulation for (self-)accelerating fluid flow through permeable medium?

I have a permeable system where is an accelerating fluid flow. Imagine a sponge that is squeezed. The fluid starts at rest, accelerates and flows out from the sponge. How to calculate the fluid speed? ...
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81 views

Configuration manifold of a rigid body

As I know, a rigid body is a set of $N$ particles in three-dimensional space subject to the following constraint: if $b_1,\dots,b_N\in \mathbb{R}^3$ are the initial positions of the particles and if $...
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89 views

car suddenly stop on hill/ circular motion

For car a it's simple, kinetic friction= mass*9.8*1.0 kinetic friction =mass*9.8 a=kinetic friction/mass=9.8m/s^2 but for car 2 is what i would like to ask about: the centripetal acceleration is v^2/...
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108 views

Trouble understanding Landau & Lifshitz writing about Lagrangians and Galilean Relativity [duplicate]

We have two inertial coordinate systems, $K'$ and $K$. $K$ is moving with infinitesimal velocity ${\epsilon}$ relative to $K'$. Using Galilean relativity we can transform this into $v'=v+{\epsilon}$. ...
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83 views

Classical Field Theory Using Geometry

I would like to know if there are good introductory courses on Classical Field Theory taught in a differential geometry approach yet one doesn't need a background in those mathematical subjects but ...
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85 views

Independence of generalised coordinates and momenta in Hamiltonian mechanics [duplicate]

I am told that in Hamiltonian mechanics, we put the generalised coordinates $q_i$ and generalised momenta $p_i$ on equal footing, and treat them as being independent from one another. But I'm ...
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136 views

Mathematics of the Virtual Displacement

So I'm pretty certain this question has been asked to death here, but I still can't find a good explanation of a very particular aspect of the virtual displacements in physics. Background For ...
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1answer
102 views

Find the separation distance for a line of oil being squashed between two flat plates [closed]

I was wondering if someone could give me some help on how to start this problem, I'm really struggling to get my head around it. A long line of oil is being squashed between two flat plates of length ...
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3answers
169 views

What was the motivation behind the work formula?

Surely there must be a reason we decided to use this as a metric for mechanical energy.How was it developed and what made it more acceptable than other work formula candidates (Like force over time, ...
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103 views

For infinitesimal Canonical Transformations, what functions are allowed for this to be a canonical transformation?

Consider two infinitesimal transformation: $$q_{i} \rightarrow Q_{i} =q_{i} + \alpha F_{i}(q,p) $$ $$p_{i} \rightarrow P_{i} = p_{i} + \alpha E_{i}(q,p) $$ where $α$ is considered to be ...
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165 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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175 views

Composing integrals in physics?

OK... so this problem isn't really specific... it's more of a conceptual puzzle. I've recently started using integrals while solving problems in physics (specifically Newtonian Mechanics and other ...
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1answer
149 views

What is the classical counterpart of an eigenstate?

Does this question make sense for every system or just some? If it makes sense, it is a periodic orbit?
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110 views

Partition function of a 3D vibrating string

Is the partition function of a 3D vibrating string a sum of discrete energies, an integral of an energy continuum, or both? $$ Z_{\text{disc}} = \sum_{k=1}^{\infty}g_ke^{-\beta E_k} $$ or $$ Z_{\text{...
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49 views

Why is a bending rod assumed to be undergoing torsion?

If I take a rod and bend it at both ends as far as it will go, why is there an assumption that I am also exerting a torsion along with my bending? Referencee: ccording to the third edition of "Theory ...
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100 views

Equations of motion for a system of $n$ particles given the potetial [closed]

I am having difficulties on the following question: The equations of motion for a system of n particles are: $$m \ddot{x}_i = - \dfrac{\partial U(x_1,...,x_n)}{\partial x_i}$$ $$\ddot{x}_i = \...
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821 views

Mechanical equilibrium : thermodynamics and classical mechanics

A similar question was asked here but mine is a bit different. In thermodynamics, a mechanical equilibrium is defined as a uniform pressure (for a fluid). In classical mechanics, equilibrium is ...
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128 views

Determining the components of the force on a curved surface due to pressure

I have a cross section of a half-tube with a pressure gradient across it causing a force outwards. I am attempting to extract the vertical component (in relation to diagram) of the force on this semi-...
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34 views

Motion in a central field in Landau Mechanics

What does this mean when E=U_eff? I don't think this means the first term in E is zero. I don't understand the sentence ' This is a cubic equation for cos(theta)'
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73 views

Classical Hydrogen Atom

I was wondering about the Hamiltonian description of the classical hydrogen atom (two point particles interacting through a Coulumb potential). In particular, I want to know if the fact that ...
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1answer
276 views

One force applied to one point of a rigid body: centre of mass and torque [duplicate]

Let us suppose that one force is applied to a point of a rigid body that is not acted upon by any other force. I think an example can approximatively be a rock in deep space, far from any relevant ...
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76 views

Continuity Equation for Momentum

Momentum is a conserved quantity, which makes me wonder if we can write an equation for the local conservation of momentum in the form of a continuity equation. If we're considering a system of ...
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1answer
84 views

Lagrangian formalism (demonstration)

My question is about the multiplicity of the Lagrangian to a Physics system. I pretend to demonstrate the following proposition: For a system with $n$ degrees of freedom, written by the ...
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1answer
172 views

Hamilton-Jacobi theory and initial value problem?

Having read through some recent posts regarding the Lagrangian formulation being interpreted into an initial value problem rather than the familiar boundary condition problem we are familiar with, I ...
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2answers
95 views

Energy drain in damped oscillator

Suppose we have a mass on a spring with a damping term. The equation of motion is given by: $$m \ddot{x} = -kx - c\dot{x}$$ I believe solutions are damped oscillations of the form: $$x = x_0 e^{-\...
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68 views

Is the force of a lifting arm due to a piston an internal force?

When I was analyzing an excavator, I was wondering if the force that the piston exerts on the lifting arm is an internal or external force. I am a bit confused because the geometry of the system ...
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126 views

Why ingoing and outgoing impact parameters equal in elastic scattering?

Take the Rutherford scattering, as for example in this picture: What is the easiest way to show that the impact parameter "b" (see picture) is the same for the ingoing and outgoing trajectories? ...
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45 views

Acceleration in a system equal for every body — why?

A 1 kg cart can slide frictionlessly on the table. The black weights each weigh 1 kg. The pulleys are frictionless. The task is to determine the acceleration of the cart. For the left-most weight we ...
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4answers
268 views

Why does this ball have potential energy at its lowest point?

A ball of radius $r_0$ starts from rest at point $A$ on the inside of a track of radius $R_0$. The question is what will its speed be when it reaches the lowest point of the track, point $B$, assuming ...
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516 views

Find angular velocity of motor

I'm quite bad at this, but I'm trying to change that and I need some assistance. Please bare with me while I attempt to explain what I'm trying to figure out and correct me where I'm wrong. Basically ...
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225 views

Star vibration frequency due to gravitation

I found the following problem on a Classical Mechanics MIT problem set, which is intended to be solved by dimensional analysis: Derive an expression for the vibration frequency of a star of mass M ...
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330 views

Work done: kinetic energy or area under F-ds curve?

Starting from $$F=ma = m \frac{dv}{dt} = m \frac{ds}{dt} \frac{dv}{ds} = m v \frac{dv}{ds}, $$ leads to work done = integral of F.ds = integral of mvdv = change in KE. Suppose a variable force is ...
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106 views

Is trajectory the same as an orbit?

Is trajectory the same as an orbit? I wanted to know about gravity assists, but most books I find are talking about different types of orbits and such. Are they related?
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500 views

Why are position and velocity enough for prediction and acceleration is unnecessary?

In classical mechanics, if you take a snapshot and get the momentary positions and velocities of all particles in a system, you can derive all past and future paths of the particles. It doesn't seem ...