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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What is the specific source(s) of sliding kinetic friction

In simplistic (K-8) physics classes, it seems to be generally instructed that the friction between two moving surfaces is due to the unevenness of each surface and the microscopic roughness. However, ...
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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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General motion of a cone on an inclined surface

Suppose that a solid cone is placed horizontally on an inclined surface and is initially at rest. How will the cone move when it starts motion due to its weight? I know that its motion depends on the ...
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Is acceleration continuous?

The extrapolation of this Phys.SE post. It's obvious to me that velocity can't be discontinuous, as nothing can have infinite acceleration. And it seems pretty likely that acceleration can't be ...
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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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U-turn in Deep Space

While writing a physically realistic game ( "Asteroid Defender" ) a physical question came up whether Diag.1 or Diag.2 or Diag.3, correctly depicts reality. In deep space (away from other celestial ...
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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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What is the problem of having an inertia tensor not satisfying the triangle inequality?

It is well known that rigid body inertia tensors are 3 by 3 positive semidefinite matrices, which is the same as saying that their eigenvalues are all non-negative. A little less known is the fact ...
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Lagrange: when a potential force, when a generalized force?

Consider the following case of a drum unrolling a mass that is on a massless string wrapped around the drum: According to my professor, here we must consider the mass $m$ being in a gravitational ...
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Taking pivot about an accelerating point

Given this question: A small ball of mass $m$ and radius $r$ rolls without slipping on the inside surface of a fixed hemispherical bowl of radius $R>r$. What is the frequency of small ...
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Deriving equations of rotational motion for connected rods

I'm working on a problem involving deriving equations of rotational motion for a system of connected rods (see the picture), and I'm a bit confused about a few things to do with rotational motion. I ...
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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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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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Is there a prediction when our solar system would fall apart?

Within a few billion years our Sun would become a red giant and destroying Mercury and Venus and perhaps even the Earth. But nevertheless our solar system will still have some planets like Jupiter and ...
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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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345 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 ...
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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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Linear momentum of a rotating system

So say we have a thin rod resting horizontally on a flat frictionless surface. The rod is pinned at its center, and a small mass collides perfectly inelastically with one end of the rod after moving ...
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38 views

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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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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1answer
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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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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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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 greater ...
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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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In real life, why is space of states or state-space defined only by position and velocity?

My book defines state-space as "the collection of all possible states of the system." For example, the state-space of a coin is heads or tails. It also said that in our world, state-space is defined ...
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In which direction does the friction act in a circular motion?

I want to know how a body moves on a circular track. Suppose a car enters a circular path. If I don't turn my steering wheel, then the car would travel in straight line and perpendicular to the radius ...
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Shooting an electrically neutral ball vs. a charged ball

If we had two identical conductive spheres of masses $m$, one with $–q$ charge and one neutral, would it take the same amount of energy to accelerate each of them to a certain velocity $v$? Uncharged ...
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Circular motion, kinetic friction and tension

Hi: I've read this post: Uniform Circular Motion w/ Tension and Friction and helped me a lot. I have a similar problem: At one end of the rope ($R = 1 m$) is tied a mass ($m = 3 kg$) and the ...
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Gravity assist, Coordinate system transformation

I am currently learning about the physics and the mathmatics behind gravity assist. I have a question regarding the coordinate transformation between the planet frame and the sun frame. I want to ...
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These components of the angular velocity are given in what reference frame?

When we have a rigid body, the rigidity constraint allows us to write the trajectory $\mathbf{r}_i$ of the $i$-th particle as $$\mathbf{r}_i(t) = R(t)\mathbf{b}_i + \mathbf{w}(t),$$ where we are ...
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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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How to efficiently cool down simulated gas by time-dependent potential?

I'm trying to simulate condensation of a highly diluted gas (a model gas, not any real one). For simplicity I restrict the simulation to 2 dimensions. To setup the simulation I take some interparticle ...
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How does a charge distribution evolve with time? (in classical electrodynamics)

It is often stated that, in classical electrodynamics, the electric and magnetic fields determine uni vocally the dynamics of a charge distribution distribution (how it evolves in time). I can more or ...
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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? ...
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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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Neglecting friction on a pulley?

So, this is how the problem looks: Plus, the pulley is suspended on a cord at its center and hanging from the ceiling. You're given masses of the objects, mass of the pulley and it's radius. And ...
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How to teach modeling physical systems?

While working as a teaching assistant for introductory experimental physics classes (newtonian mechanics and electromagnetism) for the last couple of years, I faced a certain kind of issue again and ...
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Canoe riding using your boomerang as motor

These last weeks many of us have been following the olympics. I was watching the canoe races and was impressed by the skill and energy of athletes. I thought if an olympian would have several ...
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Learning basic impact mechanics

Now I know a lot about continuum mechanics, but I still don't know why a pulse impact load damages a solid material a lot more than a constant load (i.e. a loading that varies nothing or slowly with ...