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 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 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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Is friction required for knots (not hitches or bends) to hold fast to a rope?

Using rope with idealized coefficient of surface friction approaching zero, that is in all other ways typical (typically stretchable, compressible, flexible and twistable), is it possible to tighten a ...
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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]\...
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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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Will a bullet penetrate farther through 1,000 sheets of paper with no space between the sheets, or with space between them?

Consider a gun pointed at (normal to) a 1,000-page stack of paper. Which would a bullet penetrate farther into in terms of number of pages: the stack as-is, or the same 1,000 pages stacked with spaces ...
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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 are the scalar equations for velocity and displacement if acceleration obeys the inverse-square law?

In basic high school physics/calculus you learn that you can formulate equations for velocity and displacement under constant acceleration as: $a(t) = a_0$ $v(t) = a_0t + v_0$ $x(t) = \frac{1}{2}...
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How much energy does a powerlifter need to perform a session of squats?

So I started the math myself and I'm hoping someone can look this over and improve on my idea. Let's say that a powerlifter performs the following sets of squats: % 1RM = lifted weight in percent of ...
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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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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 ...
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Weightlessness and free fall on oil drop experiment

Suppose I have an oil drop which is negatively charged placed in a box with the bottom of the box negatively charged. When this box and oil drop is placed on a table where the box is stationary, the ...
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What is the general no slip condition for rotations?

At 2:12 of this video by MIT OCW, rolling without slipping condition for a disc rotating along an axis is given as: $$ v_{cm} = \omega r \tag{1}$$ Where $r$ is the radius, $\omega$ is the angular ...
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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 ...
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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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Being Frictionless, surface of contact

I hear frequently 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 it is 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%...
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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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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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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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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 ...
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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}...
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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 $\textbf{central forces}$, ...
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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 ...
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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 ...
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1 answer
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Hanging clothes on a windy day

Hanging clothes on a windy day can be really challenging, especially if you don't have any clips lying around. Today I was hanging the clothes out in the drying area of my hostel. But soon, it turned ...
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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 ...
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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 $...
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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 ...
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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 ...
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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}\...
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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 ...
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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 ...
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1 answer
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What is the angular momentum of a double pendulum?

Is there a specific formula to calculate the angular momentum of a double pendulum?
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Confused about linear displacement in circular motion

We know that velocity is the derivative of displacement w.r.t. time. Keeping this mind, suppose that we are traveling across a circle where we go from point A to point B. In textbooks, it is said that ...
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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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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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3 answers
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Inverted pendulum on a cart - Lagrangian without moment of inertia?

I am modeling the inverted pendulum on a moving cart using Lagrangian methods. I see most examples model the pendulum's kinetic energy as a sum of translational and rotational components (using a $I\...
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2 answers
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Using Runge-Kutta method with measurements of acceleration (what to do with half-steps?)

I'd like to perform a short-time motion estimation based on measurements from an Inertial Measurement Unit. If I use the Runge-Kutta method, I will need to compute the k values at half-time steps (Ref)...
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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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How do we account for the non-net accelerations for forces in static systems?

I've googled the heck out this (as a non-physicist) and found a ton of similar questions answered but did not find anything that made the light bulb go on. I don't think I'm a crank, so here it goes. ...
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How to gradually calculate deceleration to reach velocity = 0?

I've tried to remember everything I could thats related to physics I've learned in school and college, but I'm failing. I'm currently trying to develop the physics of my own game (I could instead use ...
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Is there an egg that rolls infinitely far with no starting momentum?

This occurred to me when making an omelet. I want to construct a 3-dimensional rigid egg that when placed stationary on a flat surface with no friction or slipping either rolls to an unbounded ...
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