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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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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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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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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What happens when one uses a blender in zero gravity?

I was recently told by a friend that using a blender type apparatus in a zero gravity environment will act like a centrifuge instead mixing properly. Is this the case? Furthermore, can anyone provide ...
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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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Does an elastic massy hanging chain take the shape of a parabola?

This is a problem in "Differential Equations: A Modern Approach with Wavelets" by Krantz: If the length of any small portion of an elastic cable of uniform density is proportional to the ...
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If a ball is kept on a platform which is suspended horizontally from a helicopter, what would it take for the helicopter to drop the ball?

So I want to describe the premise better. By a helicopter I mean something that can stay suspended in air perfectly and can move around in any direction freely. To generalize the motion of the ...
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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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4answers
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Work done by constraint forces — Generalisation

Consider the above scenario: In the subsequent motion, we need to find the work done by tension on the (trolley + mass) system. Solution: Suppose at an instant, the velocity of the trolley (and hence ...
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Lagrangian equations of motion for ball rolling on turntable

The equations governing the motion of a ball of mass $m$, radius $R$ rolling on a table rotating at constant angular velocity $ \Omega $ which are derived using Newton's laws are: (I present these for ...
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1answer
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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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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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Dynamics of a bouncing capsule

I am working on a research project investigating the bounce of a capsule. I have tried to model it using conservation of energy, where we considered torque by normal force and friction during the ...
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What exactly is center of mass?

I though I understood this concept but the more I learn advanced topics like torque, momentum, work, the more I realize that I have fundamentally misunderstood it. My original, theoretical line of ...
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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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186 views

Are Electrons in a Circuit Subject to Newton's Third Law?

Consider a simple electrical circuit made up of a battery, an incandescent bulb, and wire. The battery and bulb are equal in mass and are on opposite sides of a circle made up by the wire. Lastly, the ...
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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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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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1answer
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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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Radial motions moment of inertia

I'm looking for some references on a specific moment of inertia, for radial motions of a spherical body. In my calculations, I got this integral : \begin{equation}\tag{1} \bar{I} = \int r^2 \, dm = \...
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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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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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Thermodynamics and Newton's second law

Is it correct to say, that the Newton's laws (or a Newtonian system) is reversible if the friction isn't considered (the fact that the time is of second order $\frac{d^2x}{dt^2}$) and an isolated ...
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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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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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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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1answer
381 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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1answer
556 views

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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More details on surface tension and contact angle

I am a high school student and I am very confused in surface tension , In some books it is written that contact angle is formed because the surface of a liquid can't hold tangential stress so the ...
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1answer
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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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Gravitational slingshots and energy conservation

I was watching YouTube video about gravitational slingshots and conservation of energy was explained as "planet loses its orbital energy around sun while spacecraft gains energy" In solar ...
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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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2answers
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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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3answers
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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 ...
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Deformation of an elastic ball

Suppose a free sponge ball is being compressed, due to applying a known force in a specific direction. The ball's shape will be distorted. Given are the direction of the applied force, as well as its ...
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Why does a chain or rope move the way it does when suspended and rotated on a horizontal axis?

I have always been interested in why objects like chains, ropes, etc. move the way they do when "rotated" around a vertical axis while being held only where it is suspended. It forms a shape if you ...
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Will the beaker be acted upon by the force in the direction of the green arrow?

The black circle is the top view of the beaker. In the gravity field, the beaker is vertical down along the beaker axis. The beaker is still. The water in the beaker rotates at a uniform angular speed ...
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Symmetries and conservation laws for a falling cat

For Hamiltonian systems, symmetries and conservation laws are defined and related to each other by Noether's theorem. Symmetry means the invariance of the Hamiltonian for a transformation group, and ...
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Will pyrolytic carbon/graphite repel the Sun's solar wind?

Since a moving charged particle has a magnetic field, as well as an electric field, and pyrolytic carbon/graphite repels an external magnetic field, would this mean that an object made out of ...
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1answer
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String conservation with springs

I was trying to solve this Problem that asked to find the period of small oscillations for this system. To do so I used the fact that for a massless pulley with strings around it, the sum of the ...
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1answer
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Problem regarding friction

I require a clarification on some steps in the solution of the following problem. Problem: The coefficient of static friction between two blocks shown in figure is μ and the table is smooth.What ...
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3answers
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Tension in a rotating object

I'm somewhat stuck on this very simple question, but I can't convince myself of a satisfactory answer. I tried to look through the previous questions asked to avoid asking a duplicate I hope. Any ...
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1answer
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Trouble following a chapter on harmonic oscillators (classical mechanics 5th edition)

I'm following Classical Mechanics, 5th Edition by Tom W.B. Kibble and Frank H. Berkshire. I'm following it since I'm interested in studying physics (although, am doing it at home myself). I've worked ...
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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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3answers
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Basic question on friction

Consider the whole system initially at rest. Suppose there is friction between the blocks, but not between the lower block and the floor. Suppose I apply a Force $F$ to the left over $M$, with $F$ ...

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