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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181 views

Heuristic equation for Friction force between materials

I'm programming a game where different types of objects will be sliding over different types of terrains (Top-down in two dimensions). At my current level of physics education we are given the ...
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3answers
3k 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 ...
2
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2answers
189 views

How do waves have momentum?

A question on a practice test I'm taking is as follows: By shaking one end of a stretched string, a single pulse is generated. The traveling pulse carries: A. mass B. energy C. momentum D. ...
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0answers
43 views

Hausdorff spaces and finite elements

Must the shape functions and the interpolation functions (which are the same in an isoparametric element) in a finite element model be elements of a Hausdorff space? If so, is this necessary to ...
2
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0answers
69 views

Poisson brackets and magnetic field [on hold]

I'm a maths student trying to teach myself some physics so sorry if I'm missing something simple here. I think the main problem is lack of experience with the Levi-Cevita symbol. We have a particle ...
0
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2answers
131 views

In a CMCS 2-body system, why does the speed of the particles after collision stay the same?

A particle $m_1$ is traveling with velocity $v$ toward a stationary particle $m_2$. The velocity of the center of mass is given as $v_c=\frac{m_1}{m_1+m_2}v$. Changing to a moving coordinate system, ...
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5answers
95 views

How can we explain the difference in change of kinetic energy, due to different frames of reference?

Imagine a ball ($m= 1\,{\rm kg}$) moving at a velocity $2\,{\rm m}/{\rm s}$ towards a wall. When it hits the wall, it suddenly stops, thereby liberating all its ${\rm KE}$ as heat. Here, the initial ...
4
votes
1answer
310 views

Does a thermally expanding torus experience internal stress?

I'm trying to learn continuum mechanics and thermo-mechanics. As we know, heating an object increases the mean atomic distance $a_0$ of the atoms in a rigid body. Let's assume it is a linear elastic ...
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3answers
64 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, ...
4
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1answer
111 views

Scaling arguments for the Contact mechanics between two elastic spheres

I am studying a bit granular dynamics and I have seen that two spheres of radius $R$ in contact with a contact area of radius $a$ would need an applied force $F$ on this two spheres that is nonlinear ...
4
votes
1answer
77 views

Does a Buckyball spin like an electron or like a baseball?

Does a Buckyball spin like an electron or like a baseball? We are often told that an electron does not really spin like a baseball. Only one (or two, if you count up and down) spin states, for ...
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3answers
126 views

Scalar and vector defined by transformation properties

In Classical Mechanics, we are defining scalars as objects that are invariant under any coordinate transformation. Vectors are defined as objects that can be transformed by some transformation matrix ...
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1answer
92 views

Effect of Eath's rotation on a ball thrown upwards

Since the Earth is rotating it should have acceleration (in the sense that there is change in direction of velocity). So if we throw a ball upwards won't this acceleration affect its trajectory in ...
3
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4answers
297 views

Liouville's theorem and the 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? By Liouville's theorem, the total phase space volume is ...
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2answers
33 views

Is configuration space in any similar to vector spaces?

The question may sound silly. If it is I'm sorry for it but I just couldn't find an answer anywhere else. I have just learned about vector spaces and their properties and on the other hand have also ...
2
votes
1answer
134 views

Physics of a cold and hot top

Imagine two tops made up of exactly one thousand atoms. One is kept at 4 degrees Kelvin, the other at room temperature. 1. Would they weigh the same given an arbitrarily precise scale in the Earth's ...
2
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2answers
550 views

Standing wave velocity

My question is simple: How is it that a standing wave has velocity? I mean, it's not travelling... A lot of equations depend on this concept, for example: $f_n = \frac{nv}{2L}$ Here we're ...
0
votes
1answer
332 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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0answers
16 views

What axial forces does the vertical load induce? [on hold]

What axial forces does the vertical load P induce in the members of the system down in the figure? Neglect there weights of the members themselves and assume an ideal hinge at A and a perfectly ...
0
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2answers
300 views

Advantages/Disadvantages of “hanging off” a motorcycle when leaning

The closest question I could find with regards to this subject was this one: Countersteering a motorcycle However, it does not address the specific physics of what I would like to know. There are 3 ...
8
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1answer
397 views

Reference Request: Classical Mechanics with Symplectic Reduction

I am trying to find a supplement to appendix of Cushman & Bates' book on Global aspects of Classical Integrable Systems, that is less terse and explains mechanics with Lie groups (with dual of Lie ...
0
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1answer
50 views

Why is centre of mass taken as integral of x.dm and not m.dx?

Forgive me if I'm being naive, but, I don't understand why the X-coordinate of the Centre of mass is taken as an integral of x.dm and not m.dx. I understand the summation part, but how do we convert ...
2
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2answers
54 views

How is Liouville's theorem compatible with the Second Law?

The second law says that entropy can only increase, and entropy is proportional to phase space volume. But Liouville's theorem says that phase space volume is constant. Taken naively, this seems to ...
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3answers
182 views

Instant centre of rotation for two connected gears

The two gears are have the angular velocities $\omega_1$ and $\omega_2$ respectively with respect to $Oxyz$. The task is to determine the angular velocity $\boldsymbol{\omega}$ of the arm ...
2
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3answers
102 views

Does sound have a “louder” direction?

I have a question about the propagation of sound waves. We have two TV's in our house that are almost right on top of each other. One is located on the first floor and the other one is located on ...
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3answers
5k 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 ...
4
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1answer
44 views

Without using rotational mechanics, why does a gyroscope precess the direction it does?

When a top is spun, it will precess in some direction, either clockwise or counterclockwise. It's possible to find out which way using $\boldsymbol{\tau} = d\mathbf{L}/dt$ and $\boldsymbol{\tau} = ...
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0answers
26 views

Planck's constant and phase space in quantum mechanics

During my undergrad physics classes, I've come across several seemingly related phenomena dealing with $h$ and phase space in quantum mechanics. Let $T_x$ be a translation operator by $x$ in ...
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0answers
21 views

need reference on the minimum moment of inertia [duplicate]

I would like to know if there is a book on clasiscal mechanics about the following Moment Of Inertia About Centre of Mass
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0answers
43 views

electric circuit experiment [closed]

I did the first part but a bit confused when it comes to drawing the graph for it with the table values and the conclusion to the experiment Aim:set up a series parallel network with known ...
0
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0answers
43 views

why do things stick to surfaces when left for a really long time?

I tried to move a cardboard box off the top of a cabinet, which left it on for probably years, and it was insanely difficult to remove. I don't know why this happens, but it also seems that my feet ...
1
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1answer
27 views

How does height of a parachute affect air resistance compared to circumference or diameter?

I'm trying to find out how much a double in height (making it more ovular or oblong in shape) of the parachute affects air resistance compared to a double in circumference or diameter. Can someone ...
8
votes
6answers
336 views

Why is a beam reach the fastest point of sail on modern sailboats?

I've heard that a beam reach (perpendicular to the wind) is the fastest point of sail on modern sailboats, but I haven't heard a satisfying explanation of the physics behind the claim. Triangular ...
0
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1answer
34 views

The Real Rocket

Suppose we have a Rocket with initial mass $M_o$ and we want to sent it into space. The equation of motion is (i think... please tell me if there is something i forgot) $$\frac ...
2
votes
2answers
128 views

Detailed conditions for symmetries of Lagrangian

Edit: To clarify the question, I am asking why we are justified in calling a continuous symmetry a symmetry of a system when it changes the Lagrangian by a total derivative of a function of $t, q(t)$ ...
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2answers
41 views

Independent Variables of a Lagrangian

Let us consider a particle in one spatial dimension $x$ and one temporal dimension $t$. Its Lagrangian $L$ is given by \begin{eqnarray*} L &=& T- V \\ &=& \frac{1}{2} m\dot{x}^2 - ...
2
votes
3answers
167 views

Is there an intuitive explanation of the work formula?

Upon learning calculus, I decided it was time to derive all of classical mechanics to give myself a good understanding of physics. What I found was that, while trying to do so, I would need some ...
2
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0answers
37 views

Classical Statistical thermodynamics phase space and residue $h$

In classical statistical mechanics we have to divide the partition function by a factor of $1/h^n$. In almost every calculation of a real quantity this cancels out and is thought to be a remnant of ...
0
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1answer
54 views

Why is it effectively impossible to balance this rectangle block on a triangle block? (See photo)

I've always wondered why it's basically impossible to balance a rectangle block on top of a triangle one like this. This is my nine-year-old giving it a try. I have never in my life gotten it to ...
0
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0answers
43 views

Two Particles in a Harmonic Oscillator with repulsive short-range potential

Do bear with me, I am attempting to learn to write some simulations on the computer and learn some simple MD, so I defined sort of a toy problem. I have two particles confined in a Harmonic Potential ...
0
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1answer
48 views

Basic Notation Help Needed : Classical Mechanics, Unit Vectors

Can someone help me with some basic notation? Here's a situation where I'm surely missing some trivial piece of the puzzle: Example 1: given $W = \frac{1}{2}cpAv^2$ (air resistance), adding a unit ...
0
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0answers
25 views

Magnitude of acceleration uniform circular motion

A particle moves in a plane with uniform velocity $ r' = 4 m/s$. The angular velocity is constant and has magnitude $θ' = 2 rad/s$. When the particle is $3 m$ from the origin, find the magnitude of : ...
1
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2answers
51 views

The pressure in a container of water is based on depth. So what happens if I remove the bottom of the container?

So I understand that if we have a system that involves a container of water the pressure will equal atmospheric pressure at the top and as we go further down the container the pressure will increase ...
7
votes
2answers
521 views

Why does the Stern–Gerlach quantum spin experiment conflict with classical mechanics?

My understanding of the Stern–Gerlach experiment is that neutral (0 total charge) particles are sent through a non-homogeneous magnetic field, with the expectation that the field will push that ...
0
votes
2answers
49 views

How does friction act on a body, if only 2 regions on it are rough? [on hold]

While tackling an Olympiad question, it came to my mind that friction need not act in the same direction at all points on a body. I thought of using integration to evaluate the net frictional force, ...
0
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0answers
29 views

How is the Routhian of classical mechanics defined?

The Hamiltonian is a function on the cotangent bundle to a configuration manifold $H:T^*M\rightarrow \mathbb R$. The Lagrangian is a function on the tangent bundle to the configuration manifold ...
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votes
0answers
24 views

What distance does a particle move? [closed]

I'm trying to figure out the distance that a particle moves along $x=3t^2-2t^3$ from $t=0$ to $t=4$. What method can I use to go about figuring this out?
0
votes
1answer
45 views

Why do systems with a fixed gear-ratio still use gears?

From my understanding, there are two uses of a gearing system: to change the speed of output rotation (trading it with torque), and to change the axis of rotation. Now, in a car, for example, it is ...
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1answer
62 views
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2answers
72 views

Why is sometimes more difficult to lift a baby?

I have a small cousin and she enjoys when I pick her up, which I can do pretty easily. Sometimes though she decides she wants to make my life difficult, and when she decides so, she tells me she is ...