Newtonian Definition and 327 Threads

Hi. I am self-studying GR and have many questions. Here are a few. If anyone can help me with any of them I would be grateful. 1 - What is the difference between Tu v and Tvu ? 2 - I have read that the order of indices matters in tensors but when transforming tensors from one coordinate...

Hi guys, I don´t understand too much the Newtonian limit of General Relativity. My question is: In this limit ga b (x) = ηa b (x) + ha b (x) where O(h2→0). Then, according to GR, it's straightforward to demonstrate that the Einstein equation Gt t = k*Tt t in that limit leads to Poisson equation...

Hi guys! So I am a little congused about Newtonian gravitation. I understand the equation to get a scalar for the strength of gravity, but when I plugged it into a vector field calculator (with random values of m and M), all the vectors only pointed in one way. I do understand that r-hat could...

I asked one time on this forum about bending space. If I take a paperback book and understand it as space instead of matter, and then bend it, it seems that the bent space moves into other space and that there is space from which it came. Now the idea didn't make any sense to me. Someone...

Hi all I want to ask a question about NFE(Newtonian Friedmann Equation).I know that NFE is not usefull to describe universe.But we can have a general idea about universe to use that formula. I know that the only spatial coordinate system is CMB referance frame and NFE is derived from...

Homework Statement A 1.0kg object is released form rest 500km above the earth. What is its impact speed as it hits the ground? Ignore air resistance. Homework Equations ##U_g = \frac{GmM_e}{r}## ##K = \frac{1}{2}mv^2## ## \Delta U = - \Delta K## The Attempt at a Solution Using energy...

Good afternoon all, I'm going to sound like a blithering idiot in attempting to describe my question, so please forgive me. I appreciate your patience. While working on problems in the gravitation chapter in my college physics textbook, I came across a very interesting situation that I don't...

Hi, I'm internested in a good book that teaches vectors (and perhaps tensors?) so i can better understand books on classical/Newtoniam mechanics. I know the basics of vectors, but i still get confused when i se them in physics books and don't completely understand what's going on when physics...

In friedmann equation we start to make a model kinetic energy-potantial energy=U kinetic energy depends observer and referance frame so what's the referance frame and observer in this calculation. Thanks

Homework Statement The question says that : A planet of mass ##m## moves along an ellipse around the sun so that its maximum and minimum distances from the sun are equal to ##r_1## and ##r_2## respectively. Find the angular momentum ##M## of this planet relative to the centre of the sun...

Assume we have a free-falling particle in gravity in a static metric. Its worldline is described by: g_{\mu \nu} = \eta_{\mu \nu} + h_{\mu \nu} where ##|h_{\mu \nu} << 1|##. Taken from Hobson's book: Why did they let ##g^{k\mu} = \eta^{k\mu}##?

Just a small newbie question. If Newtonian gravity is outdated and therefore inaccurate, why is it still taught? Surely the fact that Einstein's gravity is right takes priority over the fact that Newton's method is easier. Am I being ridiculous? Mahmoud.

Homework Statement See the image I uploaded. Homework Equations Paraxial approximations The Attempt at a Solution I think the image is formed after the ocular, and I understand the system is afocal. The magnification is also less than 1, but the angular magnification is >1. What I am stuck...

Homework Statement Derive Newton's and Lagrange's equation of motion for the system. Discuss differences and show how Newton's equations can be reduced to lagrange's equations. Assume arbitrarily large θ. The system is a pendulum consisting of a massless rod of length L with a mass m...

Hi everyone. Thanks for attempting the audacious challenge of deciphering the undistilled chaos that is this thread. I'd appreciate any efforts to clarify my very much flawed understanding of basic physics. 1. This is most likely a trivial question but why is the normal force perpendicular to...

Can we just combine special relativity and Newtonian gravity? If cannot, why is it intuitively not possible? If can, why is the intuition behind it? Because if can, there seems to be a need for a mediator of force for gravity which can only travel at light speed.

If Einstein proved that light (a massless object) can be bent because of space-time. Then what happens to Newton's gravitation equation F = Gmm/r^2. Obviously this cannot apply to light, so technically this should fall completely, having both Newton's and Einsteins discovery working at the same...

Homework Statement Homework Equations Navier-Stokes The Attempt at a Solution Not really trying to solve a problem, trying to understand what is going on in my textbook. So look at the stuff in red first. I see where all that is coming from, it's clear to me. However, the stuff in green...

Homework Statement Just my own personal questions concerning Newtons laws. For the most part I grasp all three laws to adequately take care of my homework, but I have some conceptual questions that keep bugging me. when solving diagrams including net forces that are acting on an object, the...

I tried searching the web for this topic but got an answer like "formulae used in classical mechanics are approximations or simplifications of more accurate formulae such as the ones in quantum mechanics and special relativity". My question is that why do the laws of Sir Isaac Newton no longer...

Hi all: In my free time, I've been playing with creating a code to help do toy simulations of gravity in my personal code of choice, FORTRAN. The first step was to get Newtonian gravity up and running and this has been pretty successful so far and I've been able to implement about 4 different...

Homework Statement Use Mach’s restatement of Newtonian mechanics to show that if we define the centre of mass of two particles according to, ⃗ r = (m1 ⃗ r1 + m2 ⃗ r2) / (m1 + m2) then the center of mass moves according to the equation, ⃗r = [(m1 ⃗u1 + m2 ⃗u2) / (m1 + m2)]t + ⃗r0 where ⃗r0 is...

The phase space of a Newtonian system is a cotangent bundle, where the base space is the manifold M of the configuration space (the positions) and the typical fiber is the cotangent space T*M (the momenta). Is it always the case that this cotangent bundle is the trivial bundle M x TM?

I have some questions regarding Newtonian spacetime; reference is MTW chap. 12. MTW translate the Lagrange e.o.m. for Newtonian mechanics (with a potential phi derived from a mass density rho via Poisson eq.) into a geodesic equation in 4-dim. spacetime. They explicitly construct the...

Recently, I've been pondering deeply on relativity (both Galilean and SR) and all of a sudden I find that I don't grasp even the basic concepts of physics (or life) anymore, i.e. I can't go back to my previous, "normal" mode of thinking. Consider Newtonian mechanics, take the ground to be at...

Consider an homogeneous spherical universe, with mass density \mathcal{\rho}_M . Then the total energy of some test-mass m at radius R(t) from the center is given by: E_{tot} = E_{kin} + E_{pot} = \frac{1}{2} m \dot{R}^2(t) - \frac{4 \pi}{3} Gm \mathcal{\rho}_M R^2(t) Or that: \Big(...

This is part of a personal project... I've recently become addicted to modeling various physical systems from scratch, such that I find explicit solutions of position as a function of time, and graph em. But I've hit a glass ceiling trying to find an analytic solution to the 1-dimensional...

If I stated a problem that you have to find the solution [0,\infty[\;\to\mathbb{R},\quad t\mapsto x(t) to the problem x(0) = x_0 < R \dot{x}(0) = v_0 > 0 m\ddot{x}(t) = -\partial_x U\big(x(t)\big),\quad\quad m>0 where R, v_0, m are some constants, and the function U has been defined...

For example at very low speed (v<<c), in Special Relativity, we can approximate relativistic motion to Classical Newtonian motion. But in General Relativity, what situation can make there an approximation to Newtonian Gravity ( just like v<<c ) ? Thanks.

So I'm looking at the hessian of the Newtonian potential: \partial^2\phi / \partial x_i \partial x_j Using the fact that (assuming the mass is constant): F = m \cdot d^2 x / d t^2 = - \nabla \phi This implies: \partial^2\phi / \partial x_i \partial x_j = -m \cdot...

Homework Statement The system in the figure uses two masses m (I will call them m1 and m2) to raise a mass M. Consider that ropes are inextensible and that the mass of ropes and pulleys is zero. Find the acceleration of each body in terms of m,M,α and g. After that, indicate what is the...

Hey guys, in classical mechanics Newton's law of universal gravitationa force says that the force between two bodies is equal to the product of their masses divided by the square root of the distance between them. So far, so good. In SR, lengths depend on the frame that we are in, and so the...

What would be the scale, in which Newtonian mechanics dissolve and QM becomes the sole victor for accurate predictions? A physics colleague told me that it was from the nanoscale to the Planck scale, but I am not entirely sure that it has been used near infinitesimally small ranges as 10^–34.

Hello everyone, I'm and English major and am writing a paper that argues our notion of progress stems from our linear perception of time. In order to make my argument I plan on citing Newtonian physics interpretation of time and then contrasting that with Einstein's interpretation of time. So...

Today, all of the scientific world (including /r/physics) buzzes about BICEP2's discovery of gravitational waves dating from Big Bang as an undispute confirmation of the general relativity. Now I wonder is it really GR? Can't it be explained by simple Newton's mechanics? I mean if you can...

I'm working through A. Zee's new EGR book, and I came to a step on tidal forces I couldn't follow. He presents the gravitational potential V(\vec{x})=-GM/r and asks us to verify that the tensor R^{ij}(\vec{x})\equiv\partial^{i}\partial^{j}V(\vec{x}) is, in this case...

Hi everyone! I've been thinking about a certain problem for a while now. And that is a Lagrangian formulation of Newtonian gravity. I know there is a Lagrangian formulation for general relativity. But I was hoping to find a Lagrangian for Newtonian gravity instead (for some continuous mass...

Homework Statement Problem in question is problem 5.6 in Dodelson's Modern Cosmology (https://www.amazon.com/dp/0122191412/?tag=pfamazon01-20) Take the Newtonian limit of Einstein's equations. Combine the time-time equation (5.27) with the time-space equations of exercise 5 to obtain the...

Homework Statement In the diagram attached a bar weighs 500 kg and is a 2D plane rigid body with mass centre at G. At the instant shown, the bar is moving horizontally at but reducing speed, causing horizontal deceleration as shown by vector a=-7i m/s2. At the same time, the bar is being...

Homework Statement A spacecraft is in a circular orbit around the moon, observing the lunar surface from an altitude of 50 km. The on board thrusters fire, decreasing the speed of the spacecraft by 20 m/s, What is the speed (in km/h) in which the spacecraft crashes into the moon...

Homework Statement Block B (1kg) is held in contact with block A (3kg). When block B is let go, A is pushed to the right with a force of 160N. Static friction is .50 between the 2 blocks. Block A pushes on B such that B is not touching the surface upon which A is moving on. It's held in the...

Homework Statement How would I go about solving this Newtonian problem? A truck is going around a circular track of radius 72m, banked at 60degrees. A spider rests on the inside wall of the truck. The coefficient of static friction b/w truck wall and spider is .91. Find the max speed that the...

Here is the question: I have posted a link to this topic so the OP can see my work.

b]1. Homework Statement [/b] 1. Two seconds after being projected from ground level (y=0 m), a projectile is displaced x=40 m horizontally and y=53 m vertically above its launch point. What are the (a) horizontal and (b) vertical components of the initial velocity v of the projectile? (c) At...

Hi guys! It is well known that the usual force based formulation of Newtonian gravity can be recast in a purely geometric form much like general relativity. This was originally done by Cartan and his theory is known as Newton-Cartan theory. Now I've tried to read up on rigorous formulations of...

Homework Statement Two triangular wedges are placed next to each other on a flat floor. Both triangles have two 45 degree angles where they touch the floor and a 90 degree angle up in the air. The Triangular wedges have a mass of m. A cube of mass M is balanced on the wedges so it's weight is...

General Relativity -- Motion in Newtonian Limit Homework Statement Assume that the metric of space-time in a weak gravitational field, \frac{\phi}{c^2} << 1 is ds^2 = (1 + \frac{2\phi}{c^2})c^2 dt^2 - (dx^1)^2 - (dx^2)^2 - (dx^3)^2 for some arbitrary scalar function phi. Use the...

1) The problem statement : For this problem, We use Newtonian Mechanics. We are placed in a geocentric frame of reference. An object (of which the mass is irrelevant for this problem) is released into the Earth's gravitational field at an altitude p(0) with no velocity whatsoever. The...

Relation between Cooling rate and Viscosity Hi all I have a situation where i have a molten Aluminium Copper alloy melt poured in a mould to be solidified. This means, the mould temperature is lower than than than the poured melt. I am thinking about a relation which associates temperature...

So for a point mass in an enclosed shell, the net force of gravity is zero (similar to electricity in a Faraday cage I presume). However, what happens when that point mass is placed in side the ring of mass m and uniform density. Say the outer shell has radius r and inner shell has radius x, so...