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Questions tagged [newtonian-mechanics]

Newtonian mechanics covers the discussion of the movement of classical bodies under the influence of forces by making use of Newton’s three laws. For more general discussion of energy, momentum conservation etc., use classical-mechanics, for Newton’s description of gravity, use newtonian-gravity.

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Can change in position due to acceleration be expressed using dual quaternions?

Dual quaternions seem like an appealing way to model 6DOF motion since they linearize rotation. I've reviewed what literature I can find on then, and found expressions for translation and change in ...
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Newton's mechanics. Axioms, postulates, etc

I am trying to write all the assumptions or postulates to set up Newton's mechanics: 1.- The space is infinite, continuous, homogeneous, isotropic and 3-dimensional. By this way, we assume that the ...
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Drifting vs. rolling when starting race

Imagine you are about to start a car race. You are on the grid, waiting for the green light. What should you do in order to optimize your start? Some people would say that a drift start would be the ...
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How can I approximate Jacobian Elliptic Functions in terms of basic integrable functions for the SO(3) rotation of a rigid body?

So, the rotation of a 3d body can be described with Euler's equations of motion giving the rotational velocity in components along the principal axes of inertia. As showed in f.ex. this paper, ...
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gravitational force for a binary of point particles with GR term

i'm trying to simulate the two body problem with 2 equal masses and I want to account for general relativistic effects. I know that the difference in the gravitational force would be an additional ...
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Do the distances from directrix and focus in a parabola shaped trajectory have a physical meaning?

According to Wikipedia, Galileo experimentally discovered that uniformly accelerated motion describes a parabolic trajectory using an inclined plane. Today we are taught at school that a ball thrown ...
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Prove from first principles that a guitar string will vibrate at a constant frequency

From experience I am aware that a taught string will generally vibrate with a constant frequency. I wanted to prove this by considering the relation of distance from the resting position, and its ...
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Torque contacts

Does anyone know the answer? Or is it rocket science or unsolvable? I experienced yesterday that when the slotted screw driver head was exact fit to the slotted screw, it was easier to turn the ...
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Explain cantilever dynamics of first mode

I would like to implement the time-dynamics of the first mode of a homogeneous cantilever, $w_1(x, t)$. I have found the equation for the first mode in wikipedia: https://en.wikipedia.org/wiki/Euler%...
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Practicality of a centrifugal space launch system

So, I read this article: https://techcrunch.com/2018/02/22/spinlaunch-2/ (TechCrunch seems to have issues with this URL: here's one from the Wayback Machine that seems reliable: https://web.archive....
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The Role of the Virtual Work Principle

Lanczos' masterpiece "The Variational Principle of Mechanics" has, on page 76, the following statement: Postulate A (virtual work): The virtual work of the forces of reaction is always zero for any ...
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Barycenter correction for inner planets in solar system?

I want to run simulations of the solar system, and I've read in some papers that to speed up the simulations it is useful to use the barycenter correction of the inner planets (from Mercury to Mars), ...
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Stability of plants and buildings: the role of the xylem

Dicotyledon plants show a stem structure with many xylem tubes, hollow but with lignified (woody) walls. These are arranged as in the figure below, in a circle. Their roots, on the other hand, have ...
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From Newton to Kepler without infinitesimals

I've read some interesting calculus-free proofs of at least parts of the derivation of Kepler's Laws from Newton's gravitational force. One is of course Feyman's "Lost Lecture" (which was already ...
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Friction of an object falling between two walls

I'm simplifying this problem into 2D for easier understanding. Lets say we have 2 vertical walls separated by distance x. Inside these walls I place an object that is only slightly smaller than x in ...
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Can one verify the Earth tide in his yard?

The ocean tide you can see on the coast. But the Earth tide beneath our feet is hardly perceivable. Is there any way to verify it in one's yard?
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Aerosol size distribution

When the size distribution of particles in an aerosol is obtained, there is always a bimodal distribution. The small peak accounts for the particles that are in sub-nanometer size range and the larger ...
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Semiflexible discrete polymer chain

Suppose we have a 2D polymer model described by a set of 2D vectors {$\mathbf{t}_i$} ($i=1,2,\dots N$) of length $a$. The energy of the polymer is given by: $$ \mathcal{H}~=~-k\sum^N_{i=1}\mathbf{t}...
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Amount of particle collisions depending on entropy

I'm doing a very simple simulation of random particles. Simple mechanics, elastic collisions. (The simulation is based on a next-event time progression.) When I count the number of particle particle ...
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Deriving the lever law using infinitesimals

I'm trying to derive the lever law by myself, however, I'm stuck. Please follow the logic of my calculations. Every object in the picture has the same mass. I want to prove that, under the effect of ...
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vibration and movement of electric appliance

So, what I am thinking about here is a cooking mixer placed into a bowl which is turned on and left moving on its own. The bowl is such that it does not topple nor the mixer falls out of it. Once the ...
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Total potential energy and equilibrium

Suppose a deformable body is under an external load. If there is no inclusion of gravity. When the body reach an equilibrium state, will the total potential energy be equal to zero? The total ...
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Horseshoe orbit cycle times

I asked on Worldbuilding originally, but was directed here instead I've been working on a habitable moon system for a story, and I'm now trying to populate the other moons around the parent planet. ...
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Max velocity before toppling risk

I want to find out the maximum velocity a machine can travel before there is a risk of toppling. Say, worst case, is that the castors hit a dead stop and the machine is brought to rest '...
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What are the fundamentals of motion in a non-inertial reference frame?

First of all, note that I understand what is considered off and on topic here. I'm posting this because I likely lack some sort of conceptual understanding of motion in non-inertial reference frames, ...
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Is angular momentum independent of axis (if axis is parallel)?

I have been told this is true for the moon on this question: Angular momentum of orbiting + rotating body but I don't understand why it should work. Surely the axis must be chosen such that the ...
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Is it possible to knock over a bowling pin without hitting it?

I bowl professionally and there is a saying when you barely hit a pin and it barely falls over. People say that you "hit it with the wind." I've been thinking, is it actually possible to knock over a ...
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How to estimate the kinetic energy loss of a rigid cube after it colliding with a heavy spring at rest?

In an environment without gravity, there is an unfixed, motionless, uniform spring with non-negligible mass m, length L, and stiffness k suspending and a rigid cube with mass M moving with velocity v ...
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Newton's Principle of Determinacy (intuitive explanation)

I was reading Arnold's Mathematical Methods of Classical Mechanics. In it he speaks of "Newton's Principle of Determinacy". He says for a mechanical system (collection of point masses in 3D Euclidean ...
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How efficient is rocket engine clustering?

So I watched a video where a guy built his own rocket from scratch. I noticed he used some F15-0 rocket engines* to get this thing as high as 300m (he's built other rockets too, where he used the same ...
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Shift a Galton board's distribution by manipulating pegs

My question is related to this one but is simpler and more specific. It's also related to this this question which doesn't answer my question. In a standard Galton board, balls are dropped onto a ...
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How can I calculate a brachistochrone-like transfer burn with a changing acceleration?

I'm working on a sci-fi story with a few locations set across the solar system, and I want to make sure that it works as accurately as possible. In order to hop from planet to planet, the ships use ...
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What are the freedom of breaking vectors into it's components?

I came across some problems in which the way I broke vectors into it's components didn't gave me answer. Here are few of them: Above mass $m$ is hanging with spring as shown, they broke $T$ in ...
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Newtonian interpretation of the Friedman-equation

I'm a first year physics student so I cannot yet understand general relativity, yet the Friedman-Lemaître-Robertson-Walker (What's in a name?) equations are used in my introductory course in astronomy,...
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centrifugal acceleration and circular velocity in curved space time

I'm studying a problem on rotation systems in general relativity. I would like to know how do these two well know newtonian formulas: $$a_{c}(r)=\dfrac{V_{c}^{2}(r)}{r},\\-\:\dfrac{\partial\Phi(r)}{\...
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What limits the speed at which elastic materials contract or expand?

Suppose a material is fixed at one end and stretched with a force within its elastic limit (so no permanent deformation occurs), what happens internally when the force is instantaneously released? ...
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What will happen to a particle in a vortex?

Consider a particle starting at rest at a position $(L, 0)$ in a coordinate system with polar coordinates (R, $\theta$). Act on the particle with a force $(0, C)$ in the same coordinates. I.e. an ...
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Where is quantum plasticity theory?

Plasticity theory (the theory of irreversible deformations) is in the world of engineering, but not in the world of Theoretical Physics is my opinion. It is therefore an entirely classical theory that ...
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Springs Properties

I want to ask for a knowledge (preferably online) source about springs properties. I would like to know how Logarithmic decrement relates to type of material and spring shape (type) and how to ...
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Motion of a catapulted point mass moving freely inside a spherical bucket

I am trying to study the motion of a point mass inside the bucket of a catapult. The catapult is shooting downward (i.e. describing a rotation of 180° from the horizontal axis) and I would like to ...
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Proof of unsolvability of $n$-body problem for $n\geqslant 3$ in general

We know there are general solutions for 1-body problem and 2-body problem and also we know in some "special cases" there are some possible solutions for $n$-body problem for $n \geqslant 3$ and there ...
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What trajectory minimizes the time traveling between two points under constant acceleration given initial and final position and velocity?

I have asked this question in the math SE but no one there knew an answer; there are similar questions here but they differ a bit from what I am trying to understand. I was wondering if there is an (...
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How does Newton's cradle with balls of different mass behaves?

Conservation of energy and momentum governs Newton cradle. If $n$ balls were lifted, $n$ balls will bounce of on the other side. This happens if all balls have the same mass. Now, assume that you have ...
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What does d'Alembert's principle actually tell us?

I have read in my book that d'Alembert's principle states: The reversed effective forces and the impressed forces at any point of a system are always in equilibrium. Now when I opt to study ...
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Foucault pendulum, where did I go wrong?

I wanted to approximate the number $N$ of periodes needed, such that the foucault pendelum turns one time. Though my result is off by the factor 2 of the results I found. What I did: I assume the ...
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How to apply conservation of energy to active noise-cancelling headphones?

Active noise-cancelling headphones add the opposite waveforms of the ambient sound in order to cancel out this ambient sound by destructive interference. I do not understand why adding more power in ...
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What happens to Newton's Third Law during the reflection of a pulse from a free end?

Well, it is known that a pulse gets inverted when it gets reflected from a fixed support while the polarity of the pulse remains same when the incident pulse gets reflected from a free end. However, ...
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Dark matter “hair” flowing through the earth

Gary Prézeau of NASA's JPL has done some calculations of how dark matter might be focussed by the Earth's gravitational field (publication preprint), and the results show some remarkable hairy ...
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Precession of angular momentum vector

I'm studying Classical Mechanics on Goldstein's book, so I'm using his terminology and notation. First I'll explain where the question comes from: consider a heavy symmetrical top and consider the ...
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Initial conditions for a massive objects to follow a path

Suppose I have a path, such as the one traced out by $r^2 = \cos(2\theta)$, and $n$ objects with mass $m$ at equidistant points on this path. What velocities should each object initially have in order ...