# What is Inertial: Definition and 496 Discussions

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. ### 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...
2. ### 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?
3. ### 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...
4. ### 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 ?

6. ### 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...
7. ### 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...
8. ### 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...
9. ### 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...
10. ### 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...
11. ### I Difference Between Locally Flat & Locally Inertial?

Are they equivalent to each other?Thank you.
12. ### 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...
13. ### 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}...
14. ### 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...
15. ### About non inertial dynamics

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!
16. ### 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...
17. ### 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...
18. ### 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...
19. ### 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...
20. ### 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...
21. ### 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...
22. ### 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...
23. ### 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...
24. ### 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)...
25. ### 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...
26. ### 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...
27. ### 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?

43. ### 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...
44. ### 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...
45. ### 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...
46. ### 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...
47. E

### Which inertial frame is used when resolving toward the centre

For simple circular motion it is common to resolve forces toward the centre and relate this to centripetal acceleration, provided that the current reference frame is inertial. However where would such a coordinate system be positioned? Since it requires one axis passing through the line...
48. ### I Inertial frames in changing gravitational fields

The man floating inside the elevator travels through space at constant velocity, and soon reaches proximity to a planet. To an outside observer, the elevator appears to change course and accelerate towards the planet, so he reasons there is a force acting on the elevator, changing its course and...
49. ### A Solved: Velocity of Isolated System in Different Inertial Sys.

A problem of an isolated system's velocity in different inertial systems, in special relativity ##\ \ \ \ \ ## In the inertial reference frame ##K##, the velocity of each component of an isolated system in ## x## direction is zero at a certain time. ##\ \ \ \ \ ## The inertial reference frame...
50. ### I Inertial Mass as Speedometer: Physics & Universe

I get that the concept of relativistic mass has sort of been deprecated in physics these days and that relativistic momentum is supposed to be seen as more well useful. So let momentum equal ##\mathtt ~~ \frac {mv} {\sqrt {1 - \frac {v^2} {c^2}}} ~~## or ##~~{mv\gamma}~~##. So mass is supposed...