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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Is it possible to cut harder material with a less hard material?

Is it possible to cut harder material with a less hard material - for example cut a steel rod with iron blade ?
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2answers
236 views

How do I figure out the momentum of a water balloon when it reaches the person I am throwing it at?

Recently an experiment was performed in which myself and a partner filled a water balloon and threw it back and forth at each other without breaking it. We gradually increased the distance at which it ...
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1answer
132 views

Sufficient conditions for the energy to be not conserved?

I'm almost embarrased to ask this question because I thought I was by now very confident with classical mechanics. Someone has stated that given a mechanical system with a Lagrangian $L$ s.t. ...
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0answers
32 views

Vectors in three dimensions [on hold]

A plane travels 40 degrees east of north from the Heliport travelling horizontally distance of 2km while reaching an altitude of 2500m and turns travels horizontally another 3km and loosing 1500m in ...
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0answers
58 views

Lagrangian mechanics is different form Newtonian? [duplicate]

I am a post graduate student and had completed my classical Mechanics with Newtonian mechanics to Hamiltonian mechanics. I have better understanding of Newtonian, Lagrangian and Hamiltonian. But I ...
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1answer
84 views

Why is the gravitational field potential scalar?

On page 48 of Carroll's Spacetime and Geometry he, before introducing "gravity as geometry", discusses the classical Newtonian equation: $F_{g}=-m_{g} \nabla \Phi$ This equation is very straight ...
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0answers
16 views

Difference between marginally stable and marginally bound orbits

I have some difficulty understanding what marginally stable and marginally bound orbits are. This is what I have understood: Stable orbits: Stable orbits occur when the 2nd derivative of effective ...
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2answers
75 views

Is angular frequency dependent on time in damped harmonic motion?

I have a doubt regarding the angular frequency of a harmonic oscillator when there is damping involved. The frequency of the oscillation changes with time in the case of damping, but I haven't seen ...
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0answers
44 views

Showing the Hamiltonian of the $\alpha$ FPU is real

I am studying the $\alpha$ FPU chain which is a model of coupled oscillators with small non-linearity. For these systems, I derived the following Hamiltonian $H$ which is given by $$ H=\sum_{j=1}^{N} ...
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1answer
24 views

Resonance of a tube of air in case of more complex shapes

I've been thinking about posting this question on Music Performance stack, but finally I think it fits more here since I'm interrested in technical details. The subject of resonance of a tube of air ...
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1answer
230 views

Vibrational anharmonic coupling and noise-induced spontaneous symmetry breaking in a hexagonal finite mechanical lattice

Happy holidays, everyone! The following is part question, part visual gallery, and part classical mechanics problem. Inspired by snow over the weekend I began simulating the vibrations of the ...
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6answers
1k views

Degree of freedom paradox for a rigid body

Suppose we consider a rigid body, which has $N$ particles. Then the number of degrees of freedom is $3N - (\mbox{# of constraints})$. As the distance between any two points in a rigid body is fixed, ...
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3answers
75 views

Motion on a frictionless vertical sinusoidal track

Today during lesson, my mechanics teacher provided a diagram of a "bowl" of the following shape: The top left and the top right have the same height, and the top right part is horizontal. He ...
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1answer
71 views

Dimension agreement in canonical transformation

In this Physics.SE post, there is a transformation: $$Q = q,$$ $$P = \sqrt{p} - \sqrt{q}.$$ for Hamiltonian $H = \frac{p^2}{2}$. The post discusses the validity of this transformation as a canonical ...
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1answer
53 views

Liquid Column “Recoils” in a Sealed Cylinder When Hit by a Piston — Is it Possible?

Consider a cylinder filled partially with a liquid (e.g. water). The cylinder is sealed, and is at held at room temperature (e.g 298K). At equilibrium (or when no external disturbance is imparted to ...
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1answer
35 views

Indicate if objects after collision will stick

Is it possible to indicate if objects after collision will stick together knowing their properties(materials,hardness,etc)?
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1answer
82 views

Is static friction an impulsive force?

For example: let's consider a static sphere on an horizontal rough surface. I apply an impulse $J$ parallel to the ground and in the middle of the sphere. If, like my book says, the friction is not an ...
2
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3answers
113 views

Is thermodynamic free energy and potential energy the same thing?

The equation for free energy $F$ and potential energy $E_{pot}$ are: $$ F=U-TS \\ E_{pot} = E_{tot} -E_{kin} $$ But the temperature $T$ is proportional to the average kinetic energy of a system. So ...
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4answers
375 views

Question about canonical transformation

I was going through my professor's notes about Canonical transformations. He states that a canonical transformation from $(q, p)$ to $(Q, P)$ is one that if which the original coordinates obey ...
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1answer
37 views

Is a motor HP torque directly proportional to the increasing HP among identical motors?

Say you have three motors: Motor 1 = .10 HP with x torque, performing task A Motor 2 = 1 HP with y torque, performing task A Motor 3 = 10 HP with z torque, performing task A If the motors are the ...
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3answers
5k views

Factors affecting torque and RPM of a motor

I am not a physics guy, so not even the basic concept of a DC motor is easy for me. My question is as follows: How do these parts of a motor affect its RPM and Torque? I had my research a while ago ...
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3answers
77 views

If a body is floating in a static fluid, then the volume of the displaced fluid equal to the volume of the inmerse part of the object (proof)

Suppose an arbitrary body is floating in a static fluid, either totally or partially immersed in it, then the volume of the displaced fluid equal to the volume of the immersed fraction of the object. ...
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1answer
55 views

Equation of motion for system of springs

I need to find the equations of motion for the following system. If $x_1$ is $m_1$'s extension and $x_2$ is $m_2$'s, then, I feel like for $m_1$ we just need to consider $x_1$ giving $$m_1 a_1 = ...
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2answers
983 views

What are the expressions for rotational and translational kinetic energies of a system of point particles?

Consider a system of point particles , where the mass of particle $i$ is $\mu_i$ and its position vector is $r_i$. What are the expressions for translational kinetic energy and rotational kinetic ...
3
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1answer
472 views

Rotating/Translating Disk

I was trying to understand an aspect of rotational dynamics and thought of a problem to help me learn. I'm sure this problem has been considered by countless people in the past, but I'm having some ...
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2answers
164 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
33 views

Sympletic transformation and Hamiltonian function

Let's say that $x:=(p,q)$ is a trajectory in phase space and $$x'(t) = J \nabla H(x(t))$$ are Hamilton's equation of motion. Now I transform $F: M \rightarrow N, x \mapsto y(x)$ diffeomorphic to some ...
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2answers
78 views

How can I derive the Hamiltonian of simple harmonic oscillator from this Lagrangian?

I'm working through Leonard Susskind's Theoretical Minimum: Classical Mechanics and I can't seem to understand how the Hamiltonian of a simple harmonic oscillator is derived from the following ...
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1answer
43 views

Initial conditions in classical mechanics

In classical mechanics, specifying the initial coordinates and velocities of all particles uniquely determines the system's future; we do not need to specify accelerations or higher derivatives. Can ...
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0answers
24 views

What forces are involved to enable a rock to skip in water?

Does the surface tension matter or is it something else that is providing the upward force? Can someone explain the phenomenon to me physically?
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3answers
514 views

What exactly is a virtual displacement in classical mechanics?

I'm reading Goldstein's Classical Mechanics and he says the following: A virtual (infinitesimal) displacement of a system refers to a change in the configuration of the system as the result of any ...
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4answers
204 views

Detecting absolute motion inside a box

This is not a contradiction and I know it is impossible but still consider a thought experiment by me and point out if something is wrong. See the following picture and then the explanation follows. ...
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2answers
515 views

Is it really impossible to calculate in advance the result of throwing dice?

Is it really impossible to calculate in advance the result of throwing dice? After all, the physics of dice throwing is in the world of classical mechanics, rather than quantum mechanics.
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0answers
22 views

Optimal size of a windmill for a given windspeed

Here is the problem: Assume that you have some constant wind speed. I want to run a windmill but I need to decide how big a windmill I want. The size is characterized by the length of the blades, $r$. ...
10
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1answer
416 views

Small oscillations of heavy string

I'm solving problem in classical field theory and I have some difficulties. I'm trying to study small oscilations of heavy string with fixed points. First of all I wrote down this Lagrangian: ...
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1answer
55 views

Liouville's theorem and preservation of topology

What might be a simple proof showing that the time evolution of the phase space volume can't lead to splitting off of the phase space volume? I don't know much about topology and stuff.
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1answer
43 views

Simplifying Friedmann's Equation

So we have one of Friedmann's equation: $$\rho_c = \frac{3H^2}{8\pi G}$$ Using This website, resources where gathered for specific times in the universe. The resources being the Hubble constant at ...
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1answer
65 views

Do waves accelerate?

Typically we think of acceleration as a particulate property but a previous question on this forum got me thinking. If we think of a wave increasing its velocity by increasing its energy/frequency ...
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1answer
57 views

Movement of a cylinder filled with water

Not long ago I was pretty bored at a dinner and I started playing with a water bottle that was not empty: I've been quite interested in its behavior when putted on its side and pushed: the bottle of ...
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2answers
39 views

What is the percentage of energy recovery in Kinetic Energy Recovery Systems(KERS) in cars?

Kinetic Energy Recovery Systems (KERS) use flywheels to recover energy from the kinetic motion of cars. They use a rotating flywheel that generates energy as it rotates- this generates the electric ...
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2answers
392 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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0answers
42 views

Any good resources for Lagrangian and Hamiltonian Dynamics?

I'm taking a course on Lagrangian and Hamiltonian Dynamics, and I would like to find a good book/resource with lots of practice questions and answers on either or both topics. So far at my university ...
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0answers
23 views

Effect of an asymmetric weight distribution on a hack squat machine

In a hack squat machine (see figure above), does it matter if I put more washers on one side? May this asymmetry cause an asymmetry of my effort in performing this exercise? For example, if I put ...
23
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4answers
4k views

Blowing your own sail?

How it this possible? Even if the gif is fake, the Mythbusters did it and with a large sail it really moves forward. What is the explanation?
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0answers
23 views

Restricted three body problem

I have the restricted three body problem, which corresponds, to the equation $ \ddot a-2\dot b -a= \displaystyle\frac{\partial U}{\partial a} $ $ \ddot b +2 \dot a-b = \displaystyle\frac{\partial ...
3
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3answers
248 views

Does the variation of the Lagrangian satisfy the product rule and chain rule of the derivative?

I have seen wikipedia use the product rule and maybe the chain rule for the variation of the Langragin as follows: \begin{align} \dfrac{\delta [f(g(x,\dot{x}))h(x,\dot{x})] } {\delta x} = \left( ...
3
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2answers
100 views

Why does pitch in a helicopter take effect 90 degrees later?

In a helicopter if you want to give it a forward pitch, you change the angle of the blades when it is in this position ---- So the two blades experience unequal lift and because o gyroscopic ...
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1answer
213 views

Quantum version of the Galton Board

If classical particles fall through a Galton Board they pile up in the limit of large numbers like a normal distribution, see e.g. http://mathworld.wolfram.com/GaltonBoard.html What kind of ...
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0answers
25 views

Confusion regarding a method of writing constraint equations

I came across a method for writing the constraint equations known as "The Virtual Work Method".I am quoting the exact language of the text(well,not exactly the exact)- Consider the atwood machine ...
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0answers
53 views