Inertial Definition and 500 Threads

In classical physics and special relativity, an inertial frame of reference is a frame of reference that is not undergoing acceleration. In an inertial frame of reference, a physical object with zero net force acting on it moves with a constant velocity (which might be zero)—or, equivalently, it is a frame of reference in which Newton's first law of motion holds. An inertial frame of reference can be defined in analytical terms as a frame of reference that describes time and space homogeneously, isotropically, and in a time-independent manner. Conceptually, the physics of a system in an inertial frame have no causes external to the system. An inertial frame of reference may also be called an inertial reference frame, inertial frame, Galilean reference frame, or inertial space.All inertial frames are in a state of constant, rectilinear motion with respect to one another; an accelerometer moving with any of them would detect zero acceleration. Measurements in one inertial frame can be converted to measurements in another by a simple transformation (the Galilean transformation in Newtonian physics and the Lorentz transformation in special relativity). In general relativity, in any region small enough for the curvature of spacetime and tidal forces to be negligible, one can find a set of inertial frames that approximately describe that region.In a non-inertial reference frame in classical physics and special relativity, the physics of a system vary depending on the acceleration of that frame with respect to an inertial frame, and the usual physical forces must be supplemented by fictitious forces. In contrast, systems in general relativity don't have external causes, because of the principle of geodesic motion. In classical physics, for example, a ball dropped towards the ground does not go exactly straight down because the Earth is rotating, which means the frame of reference of an observer on Earth is not inertial. The physics must account for the Coriolis effect—in this case thought of as a force—to predict the horizontal motion. Another example of such a fictitious force associated with rotating reference frames is the centrifugal effect, or centrifugal force.

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  1. askingask

    B Would it be feasible to make a chemical inertial confinement reactor?

    So basically, instead of using large complex pumped lasers, we use chemical lasers that have insane power output. They are used to fuse a fusion pellet. The excess energy is collected and part of it is used to prepare the next batch of chemicals needed to run the laser. What would be the...
  2. lia2

    A Burn efficiency in Inertial Confinement Fusion

    we have two different definitions for burn-up fraction related to inertial confinement fusion the fraction of the target mass that burns a fraction that is calculated on number densities how are these two related in non-equimolar case?
  3. D

    B Two-body Kepler problem where the Sun is at rest in a coordinate system orbited by another body

    The two-body Kepler problem where the Sun is at rest in a coordinate system orbited by another body: is the coordinate system an inertial reference system or not? Please no yes/no answers. A bit of elaboration is appreciated towards why and which principles apply.
  4. E

    I Understanding Spacetime simultaneity in twin paradox scenarios

    Context, To start with? You all know the original twin paradox. Quick review so nobody is confused : Original Twin Paradox: Traveling twin travels at v=0.8c out 4 light years (5 earth years pass)and then he returns home. Earth twin ages 10 years and traveling twin ages 6 because the...
  5. P

    I Conservation of Momentum versus Conservation of Velocity

    I have often wondered why Inertia , Newton's 1st Law, is not simply called Conservation of Velocity Can anyone give me a reason why it should NOT be called Conservation of Velocity ??? Conservation of Energy is valid in the absence of External Forces. Conservation of Momentum is valid in the...
  6. Ranku

    I Locally Inertial Frames: Freefall & Relative Velocities

    When an object is in freefall, it is in a locally inertial frame of reference. If two objects are in freefall, can their locally inertial frames of reference have different relative velocities?
  7. Thytanium

    I Inertial Gravity in Relativistic Geodesics - Forum Discussion

    Hello friends of the Forum. I want to ask you why the inertial acceleration in free fall in the relativistic geodesic equations is assumed equal to zero in free fall and equal to 9.8 m/s at rest on the earth's surface. On the other hand, assuming that zero acceleration in free fall, what would...
  8. Z

    How does FEM software compute inertial forces?

    Hello I have alwayes seen FEM applications for static structures while each " finite element" of a bar linkage mechanisms should be subjected also to a variable inertial force besides its constant weight how do FEM softwares compute inertial forces ?
  9. M

    Centrifugal and inertial force in centrifuge

  10. Spector989

    Solving Question through Inertial Frame: Challenges & Workings

    So i solved this question through non inertial frame but how do i solve this through inertial frame , when i used to solve only translation question when i observed through non inertial frame the main difference was in inertial frame Fnet = 0 and in non inertial frame Fnet -ma =0 (ma being...
  11. PhysicsRock

    Solving an Inertial Mystery: Angular Acceleration and Mud

    So, my idea would be that this happens at an angle ##\theta = \frac{\pi}{2}##, or quarter of a whole rotation. At this point, the wheel starts moving right again, after going to the left. Due to it's inertia, the piece of mud would want to keep it's current direction of motion and therefore fall...
  12. A

    B Deuterium combustion within inertial fusion schemes

    Hydrogen as well as Deuterium are both flammable chemically, I read that both hydrogen as well as deuterium can ignite/combust upon compression even in ordinary ICE engines. Hydrogen has been investigated and used as fuel for internal combustion engines. Now in a inertial fusion approach the...
  13. dom_quixote

    B Tangran, Inertial Mass and Gravitational Mass

    Imagine a tangran puzzle, in which an extra piece "y", identical to piece 'x', is maliciously added. No matter how hard the player tries, he will never be able to restore the game's original form, that is: a perfect square. This illustration has a clear purpose: If gravitational mass and...
  14. K

    I Hartle, Gravity pg 34: Question about Time in Non-Inertial Frames

    Hartle, gravity pg 34 " An observer in a inertial frame can construct a clock that measures the time t"*)Is time something else that exists irrespective of clocks? What we do is just that we measure it? Pg 35 " ...It's a central assumption of Newtonian mechanics that there is a single notion of...
  15. G

    I Difference Between Locally Flat & Locally Inertial?

    Are they equivalent to each other?Thank you.
  16. e2m2a

    I A Report on the Experimental Results of Inertial Effects

    I have attached [Mentors note: the attachment has been deleted] a paper (patent application number was 63/191,323 confirmation number 2211 filing date 5/20/21) that reports on an experiment that I did that strongly suggests that inertial effects can impact the speed of the center of mass of a...
  17. W

    I Energy Density in E Field: Does it Contribute to Inertial Mass?

    Hi. I'm not sure where to put this question, it concerns particles, mass-energy equivalence and various things. Classical electromagnetism seems to be as sensible a place as any. There is energy stored in an E field. Energy density (at position r, time t) = \frac{1}{2}...
  18. A

    Inertial confinement fusion (First light, NIF, etc)

    More or less all ICF schemes seem to be similar to the first artificial fusion method (also inertial) of the secondary of the hydrogen bomb. Before I present the question let me show just another ICF approach recently done. The company is called "first light fusion", Their method is essentially...
  19. D

    How Does Colatitude Affect the Direction of Coriolis Force?

    So I don't understand "due north from a position at colatitude ##\theta## " , whether how I translate it... I keep getting that direction should be radial...(toward Earth CM) This is my work: Thank you so much!
  20. LCSphysicist

    Lagrangean and non inertial frame

    I have tried to solve this problem using the lagrangean approach: $$L = T - V = m((\dot r)^2 + (r \dot \theta)^2)/2 - 0 = m((\dot r)^2 + (r \delta)^2)/2 - 0 $$ The problem is that the answer i got is the right answer at the smooth rod referencial, that is, at the non inertial frame. Now we can...
  21. J

    B A difficulty with the equivalence of all inertial reference frames

    Although I am not a physicist, I am interested in physics, and recently I've been reading about special relativity. I have a doubt about it, a difficulty I see in the equivalence of all inertial reference frames which I haven't found solved anywhere, and I've thought perhaps you in this Forum...
  22. Monsterboy

    Distance moved in two different inertial frames

    We have one elevator at rest and another moving up or down at uniform speed, so both of them are considered to be inertial frames. Taking the initial height of the coin as ##H = 0 + \frac{1}{2} g{t_1}^2## and ##H = 0 + \frac{1}{2} g{t_2}^2## ##t_1 = t_2 = t = \sqrt{\frac{2H}{g}}## in both...
  23. rudransh verma

    B Inertial vs non inertial frames

    I previously thought Earth is inertial frame and relative to Earth non accelerating frames are inertial too. But after watching this video, I came to know that it’s not the frame with respect to which we decide whether a frame is inertial or not. It’s the particle. When a particle is not...
  24. L

    I Proving Galilean Transformation for Inertial Frames

    I know we can prove that a Galilean transformation sends one inertial frame to another inertial frame, by proving ##\frac{d^2 f(\vec{r})}{d(f(t))^2} = \frac{d^2 \vec{r}}{dt^2}##, but can we prove the reverse? Can we prove that if the acceleration seen in two frames are the same, then the...
  25. cianfa72

    I About global inertial frames in GR

    Hi, starting from this thread Principle of relativity for proper accelerating frame of reference I'm convincing myself of some misunderstanding about what a global inertial frame should actually be. In GR we take as definition of inertial frame (aka inertial coordinate system or inertial...
  26. L

    B Inertial Frame of Ref & Forces: Understand Special Relativity

    In trying to understand a bit of special relativity, I want to make sure if I understand it correctly, and I came up with the following question: "Imagine you would know all forces in the universe acting upon an object, doesn't that give away the only real existing frame of reference (imagining...
  27. S

    I Counter-rotating mass to counteract inertial spin

    How do I determine the required combination of spin rate and disc mass to counteract the inertia of a second spinning disc? I have complete knowledge of and control over both disc masses and spin rate and geometry. Let's say Disc A geometry, mass and spin rate are fixed and constant, so I can...
  28. Killtech

    I Transforming Object Positions b/w Frames: A Procedure

    Let's same I have an observer A and B that initially occupy the same point at ##t=0## but they have a relative velocity to each other. Now let's assume there is an object C that moves in a circular motion around some point from A's frame. The initial condition/position is given (in A's frame)...
  29. D

    Rotation: inertial frame vs. body-fixed frame

    Hi Angular momentum L is related to the moment of inertia (MOI) , I by L= Iω In the body-fixed frame , ie. rotating with the object then ω = 0 and so the angular momentum is zero in the body-fixed frame. Is that correct ? If i have a thin circular ring then the MOI about the centre is given by...
  30. H

    A Ising lattice seen by an inertial observer

    We have an Ising lattice on the x-axis . on every site there is an atom which can be up or down. i suppose that there are N atoms (repetedly with the same values). Each sequence of spins has an energy H with a probability exp(-H/k T) i suppose that there is a device attached to each atom...
  31. Kairos

    B V=dx/dt (relative velocity between two inertial observers)

    In special relativity, when writing the relative velocity between two inertial observers v=dx/dt, I suppose that "dt" is a coordinate time interval? But as it is not measurable, is the velocity correct and the same for both observers if each one uses his proper time intervals?
  32. J

    I Metric Transformation b/w Inertial Frames: Analyzing Effects

    The metric tensor in an inertial frame is ## \eta = diag(-1, 1)##. Where I amb dealing with only 1-D space. The metric tranformation rule after a crtain coordinate chane is the following: $$ g_{\mu \nu} = \frac{\partial x^\alpha}{\partial x'^{\mu }} \frac{\partial x^\beta}{\partial x'\nu }...
  33. V

    Law of inertia (inertial observer and inertial frames of reference)

    I am trying to figure out what are inertial observer and inertial frames of reference. The law of inertia holds for inertial observers. Inertial observers are objects with zero net force acting on them, and move with constant velocity. Suppose we fix a set of coordinate axis in space, relative...
  34. J

    Electromagnetic inertial reaction force?

    I accelerate charged particle ##A## causing virtual photons to travel to distant charged particle ##B## which feels an electromagnetic force proportional to ##A##'s acceleration (for a classical field description of this effect see https://www.feynmanlectures.caltech.edu/I_28.html Eqn 28.6)...
  35. Leo Liu

    Why is angular momentum measured at a non inertial CoM conserved?

    Question 7.6 Official solution It seems that the solution uses the conservation of angular momentum to solve this question (τ=0). But the problem is that the frame is set on the centre of mass of the guy, which is non inertial. I would like to know why it is correct to do it this way. My...
  36. MPavsic

    Coriolis inertial acceleration

    I am a self learner. I have a specific question regarding the Coriolis inertial acceleration. If question is already answered on this forum please redirect me there. As depicted on the picture we have rotating platform and the chain of particles passing across the rotating platform. The...
  37. person123

    Inertial Force in Fluid Mechanics

    According to one explanation, the left hand acceleration terms of Navier Stokes equations are the called the inertial terms. If you were to balance forces on the fluid particle, they would have to be equal and opposite to the forces on the right hand side (pressure gradient, viscous, and body)...
  38. Arman777

    I Meaning of the inertial energy density

    I am reading an article, which talks about graduated dark energy (gDE) model. In this model, it's assumed that the inertial mass density exhibits power-law dependence to its energy density $$\rho_{inert} = \gamma\rho_0(\frac{\rho}{\rho_0})^{\lambda}$$ Where ##\gamma## and ##\lambda## are real...
  39. cianfa72

    I About inertial reference frames and logical deduction

    Hi, consider the following in the context of classic mechanics and SR. We know there exist special "frame of reference" according to free objects stay at rest or keep moving with constant uniform velocities. Suppose you single out a such reference frame according to the Newton law of inertia...
  40. A

    I Einstein vs Newton: The concept of inertial vs non inertial frames

    Is concept of inertial vs non inertial frame inveted in Einsten theory of relativity or Newton knows that we can see on same object from different perspective? (Newton set 3 laws for inertial frame,so did he knew for realitivtiy when view object form different perspective/frame and did he...
  41. J

    B Gravitational Mass of C/2 Objects: Jim Adrian's Inquiry

    I would like to be sure that objects passing at high speed (half or more of the speed of light) have more gravitational attraction to each other than they would if their relative speed were forty miles per hour. Thank you for your help. Jim Adrian
  42. T

    What is an inertial frame? A conflict of two definitions

    Good Morning (I see this has been discussed here, but I am more interested in two specific definitions and whether the conflict.) I had always thought that the definition of an inertial frame was: "A frame in which Newton's Laws are valid." A person has been arguing with me that the definition...
  43. A

    Is gravity an inertial force or interaction force?

    We feel that Earth pull as to the ground but is Earth accelaritng up "in some way" so gravity is also inertial force?? I read that we still don't understand what is gravity...
  44. S

    B Why is "time orthogonal to space" in inertial reference frames?

    I'm reading about the geometry of spacetime in special relativity (ref. Core Principles of Special and General Relativity by Luscombe). Here's the relevant section: ----- Minkowski space is a four-dimensional vector space (with points in one-to-one correspondence with those of ##\mathbb{R}^4##)...
  45. LCSphysicist

    Trajectory in a non inertial frame

    Well, make the center of the polar coordinates at the center of the turntable, so put r along the ro initial. I am well known that to someone who is rest on the turntable, the equations will be the follow: dr/dt = ro - vt If the turntable route with angular velocity w, dtheta/dt = -wt We...
  46. J

    I Does direct interparticle action imply advanced inertial forces?

    In his Nobel lecture (https://www.nobelprize.org/prizes/physics/1965/feynman/lecture/) Richard Feynman states that by varying the Schwarzschild-Tetrode-Fokker direct interparticle action $$A=-\sum_i m_i\int\big(\mathbf{\dot X_i}\cdot\mathbf{\dot X_i}\big)^{1/2}d\alpha_i+\frac{1}{2}\sum_{i\ne...
  47. Arman777

    I Cosmology: Inertial Reference Frames & Misconceptions

    I was reading an article about the misconceptions in cosmological horizons and I wanted to clarify an idea. https://arxiv.org/abs/astro-ph/0310808 In cosmological perspective, is there a global inertial reference frame (maybe CMB) ? Or all inertial frames are defined locally and there is no...
  48. T

    I The existence of negative gravitational plus positive inertial mass?

    The term “negative mass” gets puts forth occasionally, and it’s definitions can sometimes be unclear. the topic I’m interested in is particles which have both positive inertial mass and negative gravitational mass. So far, what theories do physicists have of speculating on the existence of...
  49. JD_PM

    A Orthogonal spacelike and timelike vectors and inertial frames

    I know that any vector ##V## in Minkowski spacetime can be classified in three different categories based on its norm ##|V| = \sqrt{V \cdot V} = V^{\mu}V_{\mu}##. These are: 1) If ##V^{\mu}V_{\mu} < 0##, ##V^{\mu}## is timelike. 2) If ##V^{\mu}V_{\mu} > 0##, ##V^{\mu}## is spacelike. 3) If...
  50. M

    I Special Relativity & No Special Inertial Frame of Reference

    As per special theory of relativity, no inertial reference frame is special! If a spaceship is moving at 100 m/s, no one can conduct an experiment to determine whether it is moving at 100 m/s or the rest of the universe is moving to the opposite direction at -100 m/s, if I understand the...
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