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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Active and passive transformations and the change in potential energy

Under active transformation, the particle moves. On the other hand, for a passive one, the coordinate is just relabel. I've read that the passive one will not affect the potential energy and the ...
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1answer
67 views

Relationship between tangential & centripetal forces when angular speed constant but radius varies

The model of a circular motion in basic Physics textbooks and online resources (e.g., Wikipedia on circular motion) assumes that the motion is a circle with constant radius to derive relationships ...
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128 views

How to understand dynamics $\dot x_i=\partial_jA_{ij}$ from skew-symmetric potential $A$?

We speak of a dynamical system with a potential if there is a scalar possibly depending on coordinate such that the vector field is exactly the (negative) gradient of the potential. That means each ...
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2answers
64 views

Internal potential energy and relative distance of the particle

Today, I read a line in Goldstein Classical mechanics and got confused about one line. To satisfy the strong law of action and reaction, $V_{ij}$ can be a function only of the distance between ...
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14answers
2k views

Why quantum mechanics?

Imagine you're teaching a first course on quantum mechanics in which your students are well-versed in classical mechanics, but have never seen any quantum before. How would you motivate the subject ...
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2answers
87 views

State of constant motion

Why does an object remains in its state of constant motion if there are no forces acting on that object? My understanding is that all the energy of the motion will be kept inside and a change in the ...
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1answer
60 views

Speed of liquid being blocked at end of pipe

How fast would water go if at the end of of a 1 inch diameter pipe was closed by a valve? The system is as follows: 5 meter high source of water that feeds a 1 in pipe. The pipe goes straight down ...
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1answer
51 views

velocity in inertial and nontial frames

I got confused about the difference between the last term of both pictures. In the first one, we have w x r, but in the second we have w x r underlined. Does anyone have a better explanation? They ...
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2answers
48 views

Query into the cumulative velocity of mounted platforms

Consider throwing a stone at an object from rest, it travels at Vms-1. Now throw that stone whilst running at Ums-1. It seems in the latter scenario the total speed of stone is V + U. Now imagine ...
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46 views

Can all the systems have a Hamiltonian description? [duplicate]

I have heard of mechanical systems that might not have a Hamiltonian dynamics, but I cannot figure out an example that supports it. Please help.
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2answers
129 views

Derivation of Lagrangian?

I know that the Lagrangian $L$ is defined to be $T-V$, i.e. the difference between kinetic energy and potential energy. Also the Action $S$ is defined to be $\int Ldx$ and from this we can derive ...
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3answers
151 views

Does mass affect velocity when travelling through frictionless medium?

I found the following question on an standardized test, and was debating with some friends what the answer would be: A car of mass M is travelling with a constant velocity through a plane in which ...
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3answers
406 views

Classical/Quantum Coin Toss

I am having a brainfreeze moment and have confused myself, help appreciated! Classical Coin: Heads OR tails. Quantum Coin: Superposition Heads AND Tails. Classical Mechanics: Deterministic (in ...
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5answers
195 views

Is an “infinitely sharp blade” possible?

A staple of science fiction and fantasy is a blade (knife, sword, ...) that cuts through literally any solid object (wood, steel, concrete, skulls, ...) without effort, often even without the need to ...
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2answers
532 views

The other side of the lever

If I have a lever, but I can see only up to the hinge and not the other half, can I know whether the other half is 1 m long with a weight of 3 kg on it, or 3 m long with a weight of 1 kg on it?
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3answers
546 views

Extended Rigid Bodies in Special Relativity

I was reading Landau & Lifshitz's Classical Theory of Fields and I noticed that they mention that an extended rigid body isn't "relativistically correct". For example, if you consider a rigid ...
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1answer
110 views

Is there a systematic way to derive constraint equations?

There's this problem in Goldstein's (Classical Mechanics) derivations section: 5. Two wheels of radius $a$ are mounted on the ends of a common axle of length $b$ such that the wheels rotate ...
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0answers
35 views

How does a simple weighing balance actually work? [duplicate]

I have made a simple sketch of how I think the system looks like. My problem is: I always thought that the angle the balance makes is a function of the difference between the two masses (or the ...
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0answers
19 views

Am I understanding power correctly? [duplicate]

4 men weighing 380kg, carrying a 380kg piano up 5 meters will generate 31 watt if the load takes 20 minutes. Now this is very hard to do and saps the strength out of any human being. However, that ...
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1answer
24 views

Do I need the exact velocity when experimenting with sliding coins?

I'm doing a home experiment but it's not going very well. I'm pushing coins on a table. I'm taking the time for how long it takes coin A to hit coin B and then I divide it by the time between them ...
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1answer
134 views

Which transformations are canonical?

Which transformations are canonical? Why do canonical transformations preserve the measure of integration in phase space?
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2answers
106 views

How are degrees of freedom and energy related in classical theory?

How are degrees of freedom and energy related in classical theory? How do we come to know that each quadratic degree of freedom classically contributes a factor of $\frac{k_{B}T}{2}$.
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1answer
55 views

Lorentz force in rotating frame of reference?

This is the common problem of a charged particle moving in a static electric and magnetic field. Say $\textbf{E}=(E_x,0,0)$ and $\textbf{B}=(0,0,B_z)$. In the inertial frame of reference, the ...
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1answer
33 views

A question about Hamiltonian phase flow

Show that if a one-parameter group of difeomorphisms of a symplectic manifold preserves the symplectic structure then it is a locally hamiltonian phase flow. Note that A locally hamiltonian ...
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4answers
321 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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33 views

I need a micro-sized clutch for a project, what are my options?

Also, what's the proper stack exchange site to ask this on? mechanics.stackexchange seems to be for motorvehicles. I'm designing an automatic guitar tuner that clamps onto my acoustic guitar. The ...
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0answers
38 views

Translation symmetry and the non-conserved momentum in Viscous fluids

Even though a viscous fluid has a translation symmetry (invariance) for its Lagrangian , it still 'waste' Linear momentum. How come ?, isn't the rule that every symmetry yields a conservation law ?
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1answer
29 views

Horsepower at certain RPM point without knowing torque?

I want to know the horsepower produced by an engine at certain RPM by knowing another certain RPM point? Let's suppose that an engine produces 200 hp at 4000 RPM, how many horsepower is produced by ...
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1answer
91 views

Complex variables in classical mechanics [duplicate]

In quantum mechanics complex numbers are absolutely essential because of the relation $$[\hat q_i,\hat p_j]=i\hbar\delta_{ij}.$$ But is complex number also essential anywhere in the formalism of ...
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2answers
114 views

How much force is required to compress air?

How much force (Newtons) is required to compress normal air in a chamber to 2 atm? For example, if I had a sealed piston pump, how much force would need to be exerted in order for the air to be ...
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1answer
96 views

How do I correctly choose signs for a falling particle?

An object falls from a height $h$ above water through air with negligible drag. In the water, the upward buoyancy exactly balances the downward gravitation force. The only remaining force on the ...
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1answer
78 views

Why are non-horizontal levers not considered to be in equilibrium?

Consider a triple-beam balance, like so: An unknown mass is placed on the left pan, and the provided weights are moved on the right until the lever arm comes to rest at an exactly horizontal ...
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1answer
58 views

Are Negative Eigen Values of a Hessian Matrix physically acceptable?

Suppose I have a Hessian Matrix of a System with 3N degrees of freedom, What are the physical significance of eigen values of the Hessian, Are negative Eigen Values physically acceptable?
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4answers
534 views

If a pendulum is on a rotating table, will a torque be generated?

Here is the set up. Very simple. A flat (i.e. horizontal table, there is no gravity) and rounded table that spins on its axis (through the center of the table). A spring mass system is now put on the ...
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1answer
238 views

Inclined plane question [closed]

An object, mass $m$ is placed on an incline, angle $\theta$. System is at equilibrium. coefficients of static and kinetic frictions are $\mu_s$ and $\mu_k$ respectively. Then: 1) What is the Total ...
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75 views

More on the closed-form for a simple pendulum

I've learnt about the simple pendulum, and while the regular curriculum only uses the linear approximation of $\sin\theta$ to obtain $\ddot\theta+\omega_0^{2}\theta=0$. I tried to find out about a ...
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2answers
3k views

Analyzing the motion of a ball rolling without slipping inside a hemispherical bowl

Consider a solid ball of radius $r$ and mass $m$ rolling without slipping in a hemispherical bowl of radius $R$ (simple back and forth motion). Now, I assume the oscillations are small and so the ...
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2answers
70 views

Eulerian Angles — Why three rotations can transform fixed frame into body frame?

"In general, if we restrict ourselves to rotations about one of the Cartesian axes, three successive rotations are required to transform the fixed frame into the body frame" The origin of our fixed ...
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2answers
54 views

horizontal motion inside a cone (cylindrical polars)

I have a question from an example we done in lecture Suppose we have a particle moving inside the surface of a cone given by $r = wz$ where $w$ is a constant, and also suppose initially the particle ...
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2answers
151 views

Galilean, SE(3), Poincare groups - Central Extension

After having learnt that the Galilean (with its central extension) with an unitary operator $$ U = \sum_{i=1}^3\Big(\delta\theta_iL_i + \delta x_iP_i + \delta\lambda_iG_i +dtH\Big) + ...
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2answers
16k views

Formula for a ball rolling down an Inclined Plane

Suppose we set up an experiment where we have an inclined ramp, and a spherical basketball. If we were to assume the ball to be perfectly round, and rolls down in a vertical manner and the situation ...
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1answer
49 views

Name of unknown effect where liquid moves when placed on a jagged surface

I recently saw a video in which a water droplet, when dropped on a jagged surface (see photo), and whilst under the Leidenfrost Effect, moved. Does anyone know the name of this effect?
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0answers
54 views

Matrix Representations of Galilean group

The general group element (in the vector representation) $$ \left [{ \begin{array} {c} \bar x^1 \\ \bar x^2 \\ \bar x^3 \\ \bar t \\ 1 \\ \end{array} } \right] = \left[ ...
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2answers
315 views

A sphere rolling down a rough wedge which lying on a smooth surface

A sphere of mass $m$ and radius $r$ rolls down from rest on an inclined (making an angle $\phi$ with the horizontal ) and rough surface of a wedge of mass $M$ which stays on a smooth horizontal floor. ...
5
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1answer
849 views

Invariance of Lagrangian in Noether's theorem

Often in textbooks Noether's theorem is stated with the assumption that the Lagrangian needs to be invariant $\delta L=0$. However, given a lagrangian $L$, we know that the Lagrangians $\alpha L$ ...
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1answer
298 views

Why is the Hodge dual so essential?

It seems unnatural to me that it is so often worthwhile to replace physical objects with their Hodge duals. For instance, if the magnetic field is properly thought of as a 2-form and the electric ...
5
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2answers
760 views

Conservation of linear and angular momentum

Suppose I have two rigid bodies A and B and they are connected by a spring which is attached off-center (thus possibly causing torques). Due to the spring a force $f$ acts on A and a force $-f$ acts ...
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2answers
337 views

Energy required to kick a planet orbiting the Sun from an elliptical to a parabolic path

I am trying to solve the following problem from Goldstein's Classical Mechanics: A planet of mass $M$ is in orbit of eccentricity $e=1-\alpha$ where $\alpha<<1$, about the Sun. Assume that the ...
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1answer
93 views

Lagrangian to Hamiltonian

I'm having some problems with an assignment where I have to state the Hamiltonian from the kinetic energy $T$ and potential energy $U$. These are as follows: ...
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2answers
856 views

Why does friction cause a car to turn?

I've had a lot of difficulty conceptually understanding the physics of how a car turns on an unbanked curve, so I'm hoping you could help me out. When a car is moving in uniform circular motion, we ...