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 this solveable? Simultaneous elastic collision of 4 objects in XY plane

I'm writing a computer program/game and can't figure something out; I want to be able to calculate the resulting velocities of 4 particles (hexagons, specifically) after they simultaneously ...
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1answer
69 views

Relative kinematics and laws of Newton

I am an engineering student and currently taking a class on kinematics and dynamics. I study at a German university so it may be that I don't translate everything correctly. In the first module of ...
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2answers
227 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 ...
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2answers
94 views

Maximum Extension of a Spring [closed]

In the given figure: m= 5kg, F = 30N, K = 700N/m In the figure shown above. the surfaces are friction-less. The blocks are initially at rest and the spring is initially in its natural length. What ...
3
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1answer
385 views

Hamiltonian Noether's theorem in classical mechanics

How does one think about, and apply, Noether's theorem in the classical mechanical Hamiltonian formalism? From the Lagrangian perspective, Noether's theorem (in 1-D) states that the quantity ...
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2answers
74 views

Energy conservation $\iff \frac{dE}{dt} = 0\ $?

If I'm asked to prove that a system is/ isn't conservative and compare it to whether or not the Hamiltonian is conserved, does that mean I need to compute the time derivative of energy $(T+U)$? Doing ...
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2answers
82 views

Explain how 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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2answers
434 views

Heisenberg picture of QM as a result of Hamilton formalism

Consider the formula for the total time-derivative of a physical value in Poisson's formalism: $$\tag{1} \frac{dA}{dt} = -\{H, A\}_{P.B.} + \frac{\partial A}{\partial t}, $$ where $\{A, B\}_{P.B.}$ is ...
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2answers
82 views

Phase space Lagrangian?

Reading out of this lecture series we define a phase space Lagrangian $\mathcal L$ to be a function of $4n+1$ variables namely $q,\dot q,p,\dot p,t$. My question is, what space is this function ...
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4answers
2k views

How far does a trampoline vertically deform based on the mass of the object?

If a baseball is dropped on a trampoline, the point under the object will move a certain distance downward before starting to travel upward again. If a bowling ball is dropped, it will deform further ...
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1answer
68 views

Can we disconnect an object from the pull of gravity using some material? [duplicate]

I have once come across a material/ substance/ compound, or something, that cuts off objects from Earth's gravitational pull. In other words, it would keep the object suspended in the air and will ...
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3answers
3k views

Why do non-Newtonian fluids go hard when having a sudden force exerted on them?

You can dip your hands into a bowl of non-Newtonian fluid but if you are to punch it, it goes hard all of a sudden and is more like a solid than anything else. What is it about a non-Newtonian fluid ...
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1answer
89 views

Coupled wheel and rod (analytical mechanics)

I am struggling with formulating the equations of motion. Consider a coordinate system with origin in $O$ ($y$ upwards and $x$ to the right), label the center of mass of rod $AB$ with $G$ then: ...
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1answer
56 views

When can an autonomous system be written using a Hamiltonian?

If I have an autonomous series of differential equations $$\tag{1} \frac{dx_i}{dt} ~=~ A_i(x_1,...,x_n)$$ with the condition that $$\tag{2} \sum_{i=1}^n\frac{\partial A_i}{\partial x_i}~=~0$$ in all ...
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1answer
46 views

Why does the following contradiction arise in Lagrangian Formalism?

If we look at the Lagrange's equation $\frac{d}{dt}(\frac{\partial L}{\partial \dot{q_i}})- \frac{\partial L}{\partial q_i}=0$ It is clear that Lagrangian is invariant under a Transformation $L ...
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2answers
487 views

Is the usually taught solution to forced harmonic motion just a special solution?

Let's say we have a mass on a spring being driven by a forcing function. Given hook's law, $F = -kx$, and a forcing function of $$F(t) = F_0\sin(\omega t) .$$ We can write: $$ m\frac{d^2x}{dt^2} = ...
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1answer
62 views

How to find equations of motion when potential is given by inverse-square? [closed]

When potential is $U=-\dfrac{a}{r^2}$ ($a>0$), how can I find $r=r(\phi)$? I'm trying to solve this problem during several hours. From $E=T+U$, and constant angular momentum $L$, I can get the ...
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1answer
302 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 ...
2
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0answers
74 views

Expansion of gauge potential on infinite dimensional manifold

I'm studying geometrical approaches to locomotion at low Reynolds number by reading the article Geometry of self-propulsion at low Reynolds number by Alfred Shapere and Frank Wilczek and found a ...
2
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1answer
97 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 ...
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6answers
10k views

Google interview riddle and scaling arguments

I am puzzled by a riddle to which I have been told the answer and I have loads of difficulties to believe in the result. The riddle goes as follows: "imagine you are shrunk to the size of a coin ...
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0answers
43 views

Higher order principle of isotropy

Let us work with classical mechanics in the substantivalist metaphysics, that is, space and time are seen as absolute. Call $n$-th order of motion any observer such that $n$ is the biggest order of ...
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75 views

When to use Hamiltonian vs Lagrangian?

I currently studying the Lagrangian and Hamiltonian formalisms in classical mechanics, but something I'm not seeing is how do I know which one to use in a given problem? After I find the Lagrangian, ...
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2answers
143 views

Does the superposition principle affect the space of quantum states?

I am confused about the set of quantum states. I have seen it written that in classical physics, the set of all states is a simplex. (I think this refers to the probability simplex.) In quantum ...
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1answer
103 views

Lagrangian, Kinetic & Potential energy with two masses connected to three springs

Two masses $m_1$ and $m_2$ are on a frictionless surface. They are connected by three springs with constants $k_1,k_2,k_3$. $k_1$ and $k_3$ are attached to walls and $k_2$ is between the masses. $k_1$ ...
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1answer
52 views

Does it take more effort to move against earth's rotation?

I know that if we stand still, we are traveling at 0 m/s relative to the Earth. But if we move against the rotation of the Earth we lower our speed, so, wouldn't we have to fight against the ...
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1answer
40 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 ...
0
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1answer
113 views

Is the strength of a muscle proportional to its cross-sectional area?

I have a question that is partially related to at least a couple of old questions: this one and this other. My question is specifically focused on the following point: why should the strength of a ...
2
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1answer
1k views

Derivation of Newton-Euler equations of motion

I am in search of a simplified version of the derivation of Newton-Euler equations of motion (both translational and rotational) for a rigid body (3D block) that has a body fixed frame and where the ...
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0answers
17 views

Optimal “Blow up” Configuration

Suppose you have three balls glued together. Two are red and one is blue. The system of balls is blown up by an explosion of pure energy (that conserves the center of mass frame) exactly at the ...
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1answer
41 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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2answers
155 views

Adding a total time derivative term to the Lagrangian

This is proof that $L'$ represents same equation of motion with $L$ through Lagrange eq. I understand $L'$ satisfies Lagrange eq, but how does this proof mean $L'$ and $L$ describe same motion of ...
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1answer
57 views

What is a point transformation?

This problem comes from Goldstein. What does $s=e^{\gamma t}q$ mean? Do I just put $q=e^{-\gamma t}s$ into the Lagrangian? But I don't know what that means. I think the point transformation may ...
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1answer
50 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 ...
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1answer
19 views

How to visualize the holonormic constraint $(\vec r_i - \vec r_j)^2 - c_{ij}^2$ = 0

A holonormic $(\vec r_i - \vec r_j)^2 - c_{ij}^2$ = 0 appears in Goldstein's Classical Mechanics Pg 12. Where $i$, and $j$ are particles, however $c_{ij}$ is not defined. How someone deduce the ...
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0answers
34 views

What is the conserved quantity?

Lagrangian $$ \mathcal{L}=\frac{1}{2}mv^2-q\Phi + q\textbf{A} \cdot \textbf{v} $$ is invariant under infinitesimal spatial rotation. In the process of calculating $\delta\mathcal{L}$, the term ...
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2answers
154 views

Force needed to push a syringe plunger: does one add force associated with downstream back-pressure to frictional plunger force?

I am trying to figure out how much force $F$ is needed to push a syringe plunger. The plunger needs to overcome the friction force $F_1$ and (a much smaller) inertia force $F_2=ma$, giving the total ...
0
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1answer
110 views

Equivalency of conditions involving angular momentum of a rolling ball hitting a wall

(59th Polish Olympiad in Physics) A ball of mass $m$, radius $r$ and a moment of inertia $I = \frac 25 mr^2$ is rolling on the floor without sliding with the linear velocity $v_0$. It hit the wall ...
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0answers
25 views

A rod on an inclined plane

(55th Polish Olympiad in Physics) A rod of length $l$ and mass $m$ was lain on an inclined plane of angle $\alpha$, on the altitude $h$ above the floor. (while $h \gg l)$ Describe the rod's ...
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15 views

A free axis of rotation

It is claimed that the free axes of rotation of a rigid body are the ones with the smallest and the largest moment of inertia. Why? How can we determine which free axis of rotation will be used?
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2answers
56 views

Metric and the Lagrangian [duplicate]

Does the Lagrangian formalism require a metric on the configuration manifold $Q$ in order to define a Lagrangian $L$ on the tangent bundle $TQ$? Further, if we specify a metric on the tangent bundle ...
0
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0answers
54 views

How does Zeno of Elea's argument on “motion” make sense? [duplicate]

Zeno of Elea (born c. 500 bce) argued so intensely about motion. In one of his arguments he claims – in simple language – "that it is impossible to slap somebody, since the hand first has to travel ...
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1answer
41 views

Every Galilean transformation can be written as the composition of rotation, translation, and uniform motion

Having heard many good things about Arnold's Mathematical Methods of Classical Mechanics, I picked it up and started going through it. While I think I understand all of the definitions he makes, the ...
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1answer
32 views

Determine the coefficient of static friction of a box

I have thought about a way to determine the coefficient of static friction of a box with centre of mass $c$. A force $\vec{F_e}$ acts on it at $c$. If I choose $c$ as my origin for a cartesian ...
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1answer
77 views

What are the mathematical models for force, acceleration and velocity?

In mechanics, the space can be described as a Riemann manifold. Forces, then, can be defined as vector fields of this manifold. Accelerations are linear functions of forces, so they are covector ...
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1answer
98 views

The g-force of common objects hitting the floor

At my friend's work they have an accelerometer which measures the force with which certain objects hit the ground. He claims that from four feet high, cell phones hit a solid metal surface with a ...
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1answer
71 views

spinning a water bottle quickly

When we spin a water bottle so quickly, why don't the water inside the bottle come out ? It has to do with the normal force and the apparent weight , i think . but plz someone explain for me how does ...
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0answers
36 views

Translation of the Mechanique analytique [closed]

Is there an English translation of the Mechanique analytique by Lagrange that is free? I have tried searching up online, however I only get French originals. The English translations seem all to be ...
2
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2answers
118 views

Pulling on a weakened rope - where will it tear?

Let's say I have a rope of 10m length and it is weakened in 3 spots: at 2.5m, at 5m and at 7.5m. Weakened means that if enough tension is applied it will tear at these points (all points are equally ...
2
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2answers
756 views

Is the change in kinetic energy of a particle frame independent?

Intuitively, I would expect the change in kinetic energy of a particle to be frame independent. It just doesn't "feel" right that between two points in time-space, one frame should measure a change in ...