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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What is this equation $f^e = f^a - \nabla U$?

Recently in a mechanics class my prof scribbled down something looked like $$f^e = f^a - \nabla U.$$ Where he claimed $f^e$ is the external force on an object, $f^a$ is the applied force on the ...
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90 views

Particle disintegration (Landau & Lifshitz)

In the particle disintegration problem in the book by Landau and Lifshit(z), it is considered a particle with velocity $\vec{V}$ in the lab frame, which disintegrates into two particles with masses ...
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118 views

Boundary of classical and quantum world

So we know that for the really small world we have quantum mechanical behavior and for big things we have classical behavior. But what is the boundary that differentiates the two? If we make a thought ...
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34 views

There is some attempt to build a magnetic flywheel (reservoir of motion)

We know how flywheel works! There is some attempt to substitute the flywheel-friction mechanism for some magnetic torque ? Exist some mechanism that uses thermal cycle of gases for generate magnetic ...
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144 views

How to analyse this mass-spring system

I'm trying to analyze this mass-spring system -- i.e. write down the differential equation governing it. As you can see, there is a block of mass $m_1$ attached to a wall by an ideal spring of ...
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194 views

Can vertical SHM occur in a system of a mass between 2 springs between 2 vertical pillars? [closed]

The problem is detailed above. I have worked through problems involving SHM in the horizontal plane, but unsure how to go about it vertically. I know the weight component would need to be ...
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113 views

Jumping vs pulling my hair upwards

Why can't I jump or fly if I pull my hair upwards, while I can jump using my legs? The way I see it, when jumping someone lifts its body using the muscles in the legs (while the feet are standing ...
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141 views

Lagrangian mechanics and initial conditions vs boundary conditions

It bothers me that many basic books on the classical mechanics don't discuss the following difference between "Newton's laws" and the "Principle of stationary action". Newton's laws can predict the ...
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2answers
491 views

What's the physical interpretation of an arbitrary normal mode for masses and springs?

Consider the following system consisting of 3 masses and 4 springs : I have learned that this system posseses three normal modes, corresponding to its three natural frequencies, say ...
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260 views

Pressure in Harmonic Oscillation

Classical Harmonic oscillator's energy depends on temperature as it equals $k_B$$T/2$. However, quantum harmonic oscillator energy is $(n+1/2)hf$. So, when T=0, quantum predicts motion. I have been ...
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188 views

Problem in Euler-Lagrange imply Newton

I'm self-studying Mechanics and I have a little problem: We can see that in Landau's book or in Wikipedia that when we inject the lagrangian in Euler Lagrange equation the term $\frac{\partial ...
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137 views

Ideal gas in ensemble

I want to calculate the phase space density for a single ideal gas particle in a microcanonical ensemble. I know that the partition function is given by the well-known expression that you find for ...
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2answers
289 views

A question regarding 3 bodies connected as a system

Let us consider three bodies of equal mass connected to each other with 2 ideal strings of length l. The three bodies are placed in a straight line In this arrangement there is 1 body connected to 2 ...
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25 views

belts and balls, correct size of holes

I'm working on a robot that has to transport a set of balls up at a 60 degrees angle. In order to do this I want to use a belt system with holes in it. Now my question is how big do these holes have ...
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2answers
174 views

How to take in to account torques applied at different points

Suppose we have a rigid body with known moment of inertia through some axis ($J$) and that there are multiple torques being applied in different points in that body. I know that for a rigid body, the ...
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2answers
558 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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192 views

Why can't angular momentum be used in flying vehicles?

If angular momentum (L) works like this animation from Wikipedia leads me to believe, why can't we put a large flywheel or several small ones on a chassis, all rotating counter-clockwise around ...
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985 views

A pendulum's rope swings and strikes a peg [closed]

So I have this problem, as far as I can tell I solved it correctly, and it's not equal to any of my answer choices. The problem is: A rope of length $L$ is attached at one end to a ceiling and at ...
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2answers
194 views

Electrical force between two objects

I tried to solve the following problem: There are 2 objects . The object m1 with charge q and the object m2 with charge q.(same charge).The object m2 is connected with a rope to the ceiling. at the ...
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71 views

Does mass equal angular momentum?

At the wikipedia pages for angular momentum ($L$) and moment of inertia ($I$) we find the equations: $$L=I \omega$$ $$I=m r^2$$ where $m$ is mass and $r$ is the distance between said mass and ...
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544 views

An intuitive proof of Bertrand's theorem

Is there a way to see that Bertrand's theorem is true intuitively. I mean without getting into too much mathematics ?
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125 views

Find pressure of liquids without making contact with it

Is there any way to find the pressure of a liquid inside a closed container without making contact with it? You can make any assumptions, like transparent container or anything, only rule, the ...
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2answers
438 views

Inertia matrix of a rod rotating about an axis [closed]

I'll provide a picture for clearer understanding. The problem is to calculate the angular momentum of the rod rotating about the z-axis. I have serious difficulties in deriving the inertia matrix, ...
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1answer
330 views

Calculate integral of motion condition with Poisson brackets

Problem statement: The Hamiltonian of a system is given by the formula: \begin{equation*} H = \frac{p_r^2}{2m} + \frac{p_\theta^2}{2mr^2} + V(r,\theta). \end{equation*} Under what condition is ...
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258 views

Forces on a helical screw?

The common screws which we use, are right handed helices, the simplest parametric equations of which are:- $$x(s)=\cos(s),y(s)=\sin(s),z(s)=s$$, with $z$-axis as the axis of the helix. My question ...
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732 views

Friction forces and sliding slabs

I have 2 questions, one generalizing the other. Question 1: Suppose we have 2 slabs resting horizontally on a table. Assume there is friction between the 2 slabs as well as between the bottom slab ...
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5k views

Normal force of loop-the-loop at the side of the circle

In the loop-the-loop ride a car goes around a vertical, circular loop at a constant speed. The car has the mass of 230 kg and moves with the speed of 300 m/s. The loop-the-loop has a radius R=20 m. ...
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Two boxes that are connected pushed by force - what happens between two boxes?

So when two boxes are connected together, and force is applied, two boxes move with the same acceleration. (assuming force is constant.) My question is, how are forces between two boxes get cancelled ...
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423 views

A rock connected to one end of string in circular motion gets released.. and what happens?

I know this is a basic question, but question: A rock is connected to one end of string and is in circular motion with the center being the other end of the string. Now the string gets released at ...
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1answer
286 views

Free body diagram of rod in sphere

I was finding the free body diagram part of dynamics quite easy until I found this question , Here's how it goes : A rod AB is placed inside a spherical shell, whose inside surface is rough. Draw ...
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202 views

Do we need infinite energy to make 2 similar charges touch only in theory?

By Coulomb's law, say if we have 2 point particles each having a charge of +1C then by the formula, F = k/(d)^2 if we need to make the distance between them zero, clearly y the formula, we need to ...
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1answer
5k views

What force does bathroom scale measure?

When you stand on a bathroom scale, I know that the force displayed is the normal force. Since it is the normal force, then technically the force displayed would actually be Fg= (mass)(acceleration) ...
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1k views

effect of atmospheric pressure on reading of a weighing scale

Let us consider a completely sealed weighing scale such that the air pressure above and below the pan of the scale are equal and is equal to 1 atm. pressure. The scale initially reads zero. Now if ...
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235 views

Energy of a cylinder rolling down a path

Problem statement: A cylinder rolls without slipping down a hill. It is released from height h. What is its speed when it come down? The cylinder mass may be completely concentrated on the radius R, ...
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806 views

if a simple pendulum is dropped in a elevator with a acceleration greater than acceleration due to gravity then what will be its frequency

if a simple pendulum is dropped in a elevator with a acceleration greater than acceleration due to gravity then what will be its frequency ? We know time period depends on frequency.
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168 views

Constant of gravity in earth fixed coordinate system

I have this problem: If the constant of gravity is measured to be $g_0$ in an earth fixed coordinate system, what is the difference $g-g_0$ where $g$ is the real constant of gravity as ...
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2k views

Stopping distance of two objects with equal Kinetic Energy

I'm working on a problem regarding two objects with the same kinetic energy. Two objects with masses of $m_1$ and $m_2$ have the same kinetic energy are both moving to the right. The same constant ...
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314 views

How to create frame of reference?

Is this possible to create a inertial frame of reference in the earth? How it is possible?
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746 views

FWHM in resonance amplitude square derivation

Consider a linear harmonic oscillator subject to a periodic force: $$ \ddot x + 2 \beta \dot x + \omega _0 ^2x = f_0\cos \omega t$$ The solution tends to: $$A \cos (\omega t - \delta)$$ where: ...
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4answers
1k views

How do you tell what forces do no work?

The total mass of the children and the toboggan is 66 kg. The force the parent exerts is 58 N (18 degrees above the horizontal). What 3 forces/ components do no work on the toboggan? I said the ...
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2answers
580 views

Hamiltonian and non conservative force

I have to find the Hamiltonian of a charged particle in a uniform magnetic field; the potential vector is $ \vec {A}= B/2 (-y, x, 0)$. I know that $$H=\sum_i p_i \dot q_i -L$$ where $p_i$ is ...
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2k views

What amount of force is needed to topple a person?

Assuming no sliding and that the shoulder is 1.2m from the feet, what force is required to topple a person weighing 70 Kg standing with his feet spread 0.9 m? If possible, please include an ...
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370 views

Speed of sound in air

Quick question. I thought that the speed of sound in air was constant, say in the right conditions of pressure and temperature, and humidity... 300 m/s. Now, if I have a sound source that moves ...
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2answers
87 views

How to show that if two masses($m_1$ and $m_2$) are connected($r_1<r_2$) with a string moving around a point A, they move with same angular velocity?

How to show that if two masses($m_1$ and $m_2$) are connected($r_1<r_2$) with a string moving around a point A( circular motion), they move with same angular velocity? In this special case if ...
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1answer
418 views

By how much will water resistance and upthrust slows down a fully submerged object?

Consider the following example: While running, I do work and I have a certain velocity and acceleration. When I'm in a pool (my feet are touching the bottom), I do the same work but, I have less ...
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1answer
134 views

Non-relativistic Kepler orbits

Consider the Newtonian gravitational potential at a distance of Sun: $$\varphi \left ( r \right )~=~-\frac{GM}{r}.$$ I write the classical Lagrangian in spherical coordinates for a planet with mass ...
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2answers
774 views

Precession of angular velocity about the body-fixed axis

My textbook mentions that under force-free motion of a symmetric top, its angular velocity vector $\overrightarrow \omega$ precesses about the $z$-axis of the body-fixed coordinate system. This seems ...
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951 views

Energy used to stop / slow an object

I'm trying to workout how much energy (if any), I use (imagining me as an efficient machine rather than a complex bio-mechanical human) when I lower or catch a weight. I understand that when I push it ...
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1answer
280 views

Horsepower achieved with multiple motors

Scenario I'm planning to build an electric motor for fun (not for any practical purpose). I recently purchased a shapeoko CNC mill kit and intend to manufacture most of the parts housing, stator etc. ...
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2answers
254 views

Having Trouble With The Principle Of Conservation Of Momentum For a Multiparticle System

I'am reading John Taylor's Classical Mechanics chapter 1 page 20 where he proves the principle of conservation of momentum which states "If the net external force $F^{ext}$ on an $N$-particle system ...