Tagged Questions

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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Why do things move? [on hold]

I mean, really, why do things even move? Despite the concepts of forces or mass, why does an object move? What is movement? Even in the smallest scales if you think, let's say a plank length, ...
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I am self-studying Goldstein's book "Classical Mechanics", and I need some help understanding the part where Goldstein discusses using Hamilton's principle to solve systems with holonomic constraints (...
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Is there a benefit in a final jump during an explosion?

When in movies a building explodes, the hero usually runs and jumps at the last possible time. Is there any benefit in this final jump? As far as I can see, the speed won't increase once the feet ...
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What is the gravitational field inside a hollow spherical cavity embedded in a solid sphere? [duplicate]

Imagine a solid sphere of radius $R$. From the inside of this sphere we remove a smaller sphere of radius $r$. The sphere can be situated anywhere inside the massive sphere. How does the gravitational ...
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What will happen to the center of mass of the human body when a person carries a weight with one hand?

What will happen to the center of mass of the human body when a person carries a weight with one hand a briefcase for example. Wouldn't the center of mass move horizontally towards the side carrying ...
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RWD Differential steering and front wheels [on hold]

I am developing a proof of concept autonomous car that will have 4 fixed wheels i.e. non mechanical steering. I will use rear wheels for drive and differential steering. My query is that when I want ...
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What is difference between variations of the work and virtual work?

I really want to know whether or not both equations are the same mathematically. I think that they are the same, I just want to be sure. (Reference: this website.)
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Movement of a box containig a particle [closed]

A small thought experiment: Imagine a rectangular box in space, containing particle, all resting at $t=0$ from your point of view. At some point in time $t>0$ the particle starts to move with ...
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High School Physics [on hold]

Two girls are standing on a bridge over a river. One girl falls freely and the other ties a rope to her legs. Both jump at the same time from the bridge. The length of the rope is more than the ...
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basic question about work exercise [on hold]

I am learning independently from Tobochnik's statistical physics text. He asks a warm up question about work: A person pushes a block up a frictionless ramp. Is the work positive, negative, ...
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Force dependence on velocity : Drag

I just listened to the second lecture of Leonard Susskind on classical mechanics where he discussed that force can't be proportional to velocity, since it's unable to retro-dict (predict past). He ...
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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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Airplane on a treadmill - Variant Thought Experiment

This thought experiment is in a way related to the (in)famous airplane on a treadmill problem. If you take a ball and place it on a treadmill, will the ball: Move backwards relative to the ground ...
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Motion of water droplets on airplane window during takeoff

I observed this while on a flight that took of shortly after it had rained, but could not understand why it happened. The windows of the aircraft had drops of water on the outside. As the flight ...
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Determining constants of motion for this Hamiltonian? [on hold]

Let $S$ be a Hamiltonian system with three degrees of freedom, let $q_1, q_2, q_3$ be the generalized coordinates. Suppose the Hamiltonian of the system is  H = \alpha \sum_{i=1}^3 p_i + V(q_1^2 + ...
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Uniform chain falls off table Diff EQ

I really need some assistance setting up this problem. any assistance would be a Godsend: a uniform heavy chain of length a initially has length ...
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Force and Energy in robots

There are two similar and hypothetical robots that move with wheels powered by motors, Robot A and Robot B. Robot A has a gear ratio of 3:1 (The gear connected to the motor is three times larger than ...
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Minimum initial vertical velocity of a projectile

A basketball is launched by a person with an initial velocity $v$ at an angle $\theta$ from a height $L$ into a basket of height $H>L$ which is a horizontal distance $d$ from the person. ...
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Forces Create Angular Acceleration And “Straight” Acceleration - But How Much Of Each?

Let me set up the following problem for a rectangle floating in space: We know its dimensions. We know its mass. There's a force pushing it for a known amount of time - we know the angle & ...
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Numerical solution of Duffing’s equation [closed]

Any one can help me with the Numerical solution of Duffing’s equation on urgent basis as i need this for my exam.
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Why don't hexapods gallop?

I haven't observed any terrestrial hexapods that gallop like agile tetrapods(cheetahs/horses). Instead, I've observed that all of them scuttle which constrains their maximum velocity. And after ...
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Movement of a bobbin thread when pulling it's thread at certain angles [closed]

The problem: You try to move a bobbin thread by pulling it by it's thread. If you pull it while the thread is horizontal it slides your way but if it is at an angle the bobbin thread starts rolling ...
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Physical Interpretation of the Graph of the Legendre Transform?

See Making Sense of the Legendre Transform and Legendre Transforms for Dummies. Look at the following diagram from the first link: I was trying to think of the simplest example to interpret this ...
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Will a tennis ball go further if i hit it with the side of the racket?

If i hit a tennis ball 'properly' on the stringing, does it go further than if i rotate the racket 90 degrees in my hand and hit the ball with the same force, but on the side of the frame? I'm ...
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Why does galilean invariance imply that particles that start rest stay on the same line?

I'm reading Arnol'd for self study. I'm struggling with this question: "Show that any system of two particles will remain on the same line that connected them at the initial moment, if they started at ...
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Why does overall action need to have an extremum?

Quoting from Landau's and Lifshitz' Mechanics : The integral ${\int\limits_{t_1}^{t_2}}L(q, \dot{q},t)\,dt$ for the entire path must have an extremum, but not necessarily a minimum. This, ...
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Does Special Relativity require a “ruler postulate” analogous to the “clock postulate”?

It's fairly well known that the clock postulate is needed in Special Relativity when dealing with accelerated clocks, so does something analogous exist when dealing with accelerated spatial ...
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Distinguishing mechanical systems from general dynamical systems

In the following let a "mechanical system" be a system of $n$ spatial objects moving in physical space. Consider you are given a function $q:\mathbb{R} \rightarrow \mathcal{M}^n$ with $\mathcal{M}$ a ...
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Why does my door shut faster when the window is open?

I've noticed that if I shut my door when the window is open in a room, the door will tend to shut faster. If I shut the door when the window is closed with a normal force it will not fully close as if ...
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Does the motion of a free electron in a plane wave electromagnetic field have analytical solutions?

Does the motion $[x(t), y(t), z(t)]$ of a free electron in plane wave electromagnetic field have analytical solution (oscillating E and B fields)? The Lorentz force is : \begin{align}m_e\begin{...
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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 ...
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Sliding sphere wear shape

Please refer to the figure attached. Consider a normal force is acting on the top of sphere. A constant coefficient of friction causes frictional force throughout the sliding. I want to know after ...
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Rotation matrix for aligning x-axis in an arbitrary direction

I want to align the x-axis of my coordinate system, with an arbitrary direction in space $\hat{n}$. About which axis should I rotate? Ceratinty rotation about x-axis or $\hat{n}$-axis will not serve ...
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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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Hamilton-Jacobi problem

In analytical mechanics by Fasano and Marmi they consider the Hamilton-Jacobi equation for a conservative autonomous system in one dimension with the following Hamiltonian, H=\frac{p^...
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In a 2D problem with a thrown object, why is the acceleration along the x-axis equal to 0?

I'm starting Physics, and I don't understand why the acceleration along the x-axis is zero for an object thrown near the surface of the Earth. This may be problem specific, but I wouldn't know since I ...
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Ehrenfest Theorem and boundary Conditions

In what cases does Ehrenfests Theorem hold? If I look at the wavefunction of electrons in a squared box of length $L$ (with periodic boundary-conditions, $\Psi(0) = \Psi(L)$), then the solution to ...
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Equations of motion for double spherical pendulum simply?

I am attempting to simulate a double spherical pendulum, i.e. a combination of the spherical pendulum and the double pendulum. I understand that the equations of motion can be derived via the ...
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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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Potential energy from opposing magnets repelling each other with a gap of 1 mm

I have two powerful rare earth magnets, that are separated by a distance of 1 mm. I applied energy to bring them closer to each other, hence increasing the potential energy. Now, when one of the ...
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Eigenvalue equation for kinetic and potential energy

In Boas' Mathematical Methods there is a section on linear algebra in which it is stated that we can write the eigenvalue equation for a set of springs using the kinetic energy and the potential ...
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Marvin the Martian vs. the Death Star: how much energy will they actually need to disintegrate the Earth?

According to a detailed analysis by Dave Typinski, Marvin the Martian’s Illudium Q-36 Explosive Space Modulator will require $1.711 \cdot 10^{32}~\text{J}$ to shatter the Earth into a gravitationally ...
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Fracture Mechanics: Relation between delamination and incident pressure

I am working with thin film self replicating cracks wherein a film is placed on a substrate, and the delamination and crack propagation occur simultaneously. I intend to map out the force vector field ...
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Measuring force of a punch

I'm trying to build a device that can mesure the force of a punch. ​ My initial plan was to build a platform with 4 springs (one at each corner) and an accelerometer in the middle. But, if the ...
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In d'Alembert's principle, how that the Reverse effective force and Force of constraints are different?

In d'Alembert's principle, how that the Reverse effective force and Force of constraints are different? Both are opposition or restriction on the body but how both be different in real?
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Coriolis force in free fall

Does the coriolis force has any measurable effect in free fall from large heights? Take for example the sky diving experiment by F. Baumgartner who started from a height of about 40 km above New ...
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What is the physical relevance of the classical limit to a quantum field theory?

We know the physical relevance of the classical limit of quantum mechanics quite well. However, if I take the classical limit of a quantum field theory, the answer is not so clear. Suppose I take the ...
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How to popularly describe typical features of a “non-linear system”

To quote Physics.SE tag definition: The term non-linear or nonlinear has several definitions but is generally used to describe a system that cannot be approximated by a superposition principle or ...
I'm studying Classical mechanics on Arnold's "Mathematical Methods of Classical Mechanics". In a problem i'm asked to find for which $\alpha$ the circular orbits in the central field problem are ...
A system is completely integrable (in the Liouville sense) if there exist $n$ Poisson commuting first integrals. The Liouville-Arnold theorem, anyway, requires additional topological conditions to ...