Questions tagged [newtonian-mechanics]

Newtonian mechanics discusses the movement of classical bodies under the influence of forces by applying Newton’s three laws. For more general concepts, use [classical-mechanics]. For Newton’s description of gravity, use [newtonian-gravity].

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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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How can I approximate Jacobian Elliptic Functions in terms of basic integrable functions for the $\operatorname{SO}(3)$ 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 shown in f.ex. this paper, Euler ...
Bruno KM's user avatar
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Physics of the dead man's (or jellyfish) float

This question arised during a discussion with a friend, when I discovered that he cannot do the dead man's (or jellyfish) float, i.e. float horizontally on the water, not even when he was a child. ...
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What is the symmetry group of Mach's spacetime?

Newtonian spacetime can be modeled as a geometric object $M$ (affine space or manifold with connection with an absolute time function etc. etc.) that is symmetric under the action of the Galilean ...
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Euler-Lagrange equations for chain fountain

Most of us are familiar with chain fountains. I was wondering how this phenomenon is explained in the Lagrangian mechanics. I mean do we know how the Euler-Lagrange equations look like for this system?...
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Question about the Newtonian limit of general relativity

I ran into something peculiar while attempting to carefully derive the Newtonian limit of general relativity, specifically for the geodesic equation. To set it up, we assume that the curve $q:[a,b]\...
Jonathan Clark's user avatar
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What happens if you're sitting in a wheelchair and you turn only one wheel?

My friend was sitting in a wheelchair, with a cup of coffee in one hand. That made me wonder, how would the wheelchair move if he turned only one rear wheel? He tried it, using his right hand to turn ...
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Does the Taylor series for the $N$-Body Problem converge?

So I am doing a Presentation on the $N$-Body Problem for my Physics final (12th grade) and the main content of the Presentation is going to be the comparison between an analytical and a numerical ...
SIMONE ESPOSITO's user avatar
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What is the physical motivation behind the mathematical definition of an inertial system?

In this German Classical Mechanics lecture by Frederic Schuller, it is given that a Newtonian spacetime with an absolute inertial frame is one in which $$ \nabla_{v} G=0$$ Where $\nabla_v$ is the ...
tryst with freedom's user avatar
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Reaction force exerted by pulley's support

Consider an in-extensible string passing over an ideal pulley connected to a block of mass $m$ as shown: The ends are pulled with a force $F$ Am I correct in saying that the block will experience a ...
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Criteria on good inertial system approximation

I'm currently wrapping my head around Newton's First Law. I think I start to get a basic understanding on the meaning of this law in terms of "the existence of inertial system". Basically my ...
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What would the ideal amount of gravity be for an Olympic sprinter?

The goal here is to get the sprinter running as fast as possible. How much of an effect would more or less gravity have on the top speed of an Olympic sprinter, say... Usain Bolt? 6 ft 5 in (1.95m) ...
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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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Book recommendation for classical Newtonian gravity

I’m looking for a good textbook that covers Newtonian Gravity in detail (preferably advanced undergrad/grad level). One that covers important things like Calculating trajectories of satellites around ...
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What are the maximum spring lengths of a double spring pendulum?

NOT a duplicate of Maximum length stretch of vertical spring with a mass?, I am asking about a system with two connected springs, as shown in this diagram For a single spring, you can simply equate ...
Christoffer Corfield Aakre's user avatar
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Why is $mg$ split into components instead of the tension in vertical uniform circular motion?

I am a beginner physics student. I am trying to prove that the magnitude of the tension varies sinusoidally as an object P travels around the circle or something of that sort. Thus, I am evaluating ...
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Equipartition and coupled harmonic oscillator system

This question has to do with analyzing how equipartition sets in for a system such as a coupled harmonic oscillator system. Take, for example, a system as shown in the figure: $\xi$ denoting the ...
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What are the reasons behind the different period in vertical and horizontal circular motion?

Why does hand-spinning a small mass in a vertical circular motion produces different period if the same mass is spun in a horizontal circular motion given that the radius, slotted mass are kept the ...
Sarah V.P's user avatar
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Is centripetal acceleration independent of linear acceleration in accelerated circular motion?

Can we say that there is a relationship between them, or are they independent of each other? why? Like does $a_c=v^2/r$ imply $a_c$ and $a_{tangential}$ are related? I am very confused by this ...
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Being Frictionless, surface of contact

I frequently hear references to a smooth surface, or frictionless pulley. Can being frictionless be obtained if only one of the 2 surfaces has 0 coefficient of friction? Or is it for the contact of ...
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What are pre-collisions and post-collisions in forces and momentum?

What are pre-collision and post-collision exactly? I assume it is before collision and after collision. I can not find an answer on google.
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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%...
Aleksejs Fomins's user avatar
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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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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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Projectile, air resistance and wind

So for my school project I am working on a projectile simulator and air resistance. So I have looked at this. Equations for an object moving linearly but with air resistance taken into account? ...
ObnoxiousFrog's user avatar
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1 answer
485 views

How to measure gravitational acceleration in airplane?

I want to see (actually: show to my kids) evidence of the $1/r^2$-decay of gravitational acceleration by measurement, in a way as simple as possible. So I was thinking of measuring gravitational ...
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Fluid dynamics tsunami

I have been given a energy head (pressure) in meters for a given tsunami on land. If the tsunami hits a wall 1 meter by 1 meter, is it possible to calculate the height it will reach. I am thinking it ...
user50180's user avatar
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2 answers
399 views

Newton's first law and Inertial systems

Newton's first law is part definition and part experimental. Isolated bodies move uniformly in inertial systems by virtue of the definition of an inertial system. In contrast, the assertion that ...
R004's user avatar
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Why is mass nonnegative/is the nonnegativity of mass a convention?

In An Introduction to Tensor Calculus and Relativity, Lawden provides the definition of mass by considering a collision between two massive particles $p$ and $q$ with masses $m_p$ and $m_q$, ...
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What weight does a scale show when you throw an object onto it?

Imagine you have a bucket (cross-sectional area $A$) on top of a scale. Into the bucket you begin to pour sand (density $\rho$) with a mass flow rate of $\dot{m}$. The total weight of the sand in the ...
S. Green's user avatar
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1 answer
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Information theory in classical mechanics

I've only ever heard about information theory being used in stuff related to probability distributions, which makes sense because information and entropy are related. However, I'm having trouble ...
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Mechanics behind Pringle Ring

Everyone knows about the famous Pringle Ring Challenge Does anyone know how I could develop a theoretical model to predict its stability?
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Why the body don't fall down in Loop-the-Loop Situation?

In Ramamurti Shankar playlist fundamentals of physics he talked about Loop-the-Loop example which is if a trolley in a roller coaster and it's at the top of it why the roller coaster didn't fall down ...
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Kasteleyn orientation in Dimer model

Some Background: The problem of dimer configurations or perfect matching occurs naturally when a diatomic gas is adsorbed onto a crystalline substrate and was first discussed by Rushbrooke and Fowler. ...
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The Newtonian limit of torsion

Torsion is a common modification to general relativity. It is loosely described as gyroscopes twisting along geodesics. A gyroscope is basically a mass-spring system. The masses making up the spinning ...
Kevin Kostlan's user avatar
3 votes
2 answers
349 views

Angular Momentum and Coefficient of Restitution

If there was a situation where you had two rods pinned in the center and the left rod having an initial angular velocity $\omega_1$, and the right rod was at rest. I am wondering what the final ...
aero_student_EV's user avatar
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About the equation $\frac {d^2} {dt^2}\vec x(t) = \nabla \times \vec F(x(t))$. Motion in a curl vector field

I was wondering if there is a physical interpretation of ODEs of the form $$\frac d{dt}\vec x(t)=\vec y(t)$$ $$ \frac d{dt} \vec y(t) = \nabla \times \vec F(x(t))$$ (or equivalently $\frac {d^2} {dt^2}...
Overflowian's user avatar
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Particle in "external potential" VS particle on "curved surface": equivalence?

Let's consider a non-relativistic particle - its position is $x(t)\in \mathbb{R}^n$ - in an external potential $\phi$, with Lagrangian $$L=\dot{x}^i \eta_{ij}\dot{x}^j/2 - \phi(x),\tag{1}$$ where $\...
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Help with Newton's 3rd law

I am using the book Classical Dynamics of Particles and Systems by STEPHEN T. THORNTON, JERRY B. MARION and they say that Newton's 3rd law only applies when forces are $\textbf{central forces}$, ...
Reuben's user avatar
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Intuitive explanation on why velocity = 0 for a inverted pendulum on a wheel system

I believe I have solved below problem. I am not looking for help on problem-solving per se. I am just looking for an intuitive explanation. Problem statement: wheel mass = $m_1$, even mass rod BC mass ...
Josh Bolton's user avatar
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Equation of motion for a coil around a mass, attached with a spring driven by magnetic field?

First of all, thanks for reading and hello! First time poster on Physics Stack Exchange. I'm an electronics engineer (so forgive my poor maths below!) and tend to hang out there. I have a questions ...
JustAnEngineer's user avatar
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1 answer
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Do these Lagrange equations of 1st kind exhibit numerical instabilities?

I followed the lead of "Theoretische Physik", 1e, 2015 by Bartelmann et al. (pp. 171 - 174) to form the set of constituting Lagrange equations of the 1st kind for the double pendulum: eight ...
Max Herrmann's user avatar
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Can we use relative motion if acceleration of two bodies are different?

Suppose, on the $x$-axis, a body $A$ is moving with velocity $v_1$ and acceleration $a_1$, and a second body $B$ is moving with velocity $v_2$ and acceleration $a_2$. $B$ is at a distance of $S$ from $...
Pandey Shourya Prasad's user avatar
3 votes
2 answers
160 views

Pseudo Torque on a Pure Rolling Body

If we consider all the torques about instantaneous axis of rotation (which itself is accelerating) of a pure rolling disc, then should we also consider the torque by pseudo force that acts due to ...
Lekha Tv's user avatar
3 votes
0 answers
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Struggling to prove Newton's Law of Gravitation starting from smaller bodies

I have seen at least four different posts in this website in which the OP asks for a proof of Newton's Law of Gravitation (often without stating from which axioms the proof should start) all of which ...
Sam's user avatar
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1 answer
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What are virtual and apparent forces?

Acceleration in a rotating frame can be written as: $$\underline{a}=\frac{\partial^2\underline{r}}{\partial t^2}+\frac{\partial\underline{\omega}}{\partial t}\times\underline{r}+2\underline{\omega}\...
Alex Hughes's user avatar
3 votes
1 answer
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Can a pendulum at resting equilibrium position still demonstrate the Earth's rotation?

I conducted an experiment in my youth, creating a 'sand pendulum' hanging from the bedroom ceiling to a bowl of flour. I did not set the pendulum into motion, but rather wanted to see if the force of ...
Conor Murray's user avatar
3 votes
1 answer
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Mechanics: what does work done against resistance really mean?

Does ''work done against resistance'' mean the force needed to overcome friction i.e. the magnitude of the frictional force itself x distance? or does it mean the work done by the net force i.e. (the ...
ilove cupcakes's user avatar
3 votes
1 answer
188 views

Average energy of an SHM

Why do we usually calculate the average potential or kinetic energy of a simple harmonic motion with respect to time, why not with respect to position? Why even calculate average energy for an SHM? ...
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