# inertial frame Definition and Topics - 26 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. ### Pendulum hung from the ceiling of a train

(a) No, a person seated inside the train compartment will not be able to tell whether the train is accelerating on a horizontal track or moving uniformly up an inclined track by observing the plumb line. (b) I am assuming that both observers are not allowed to look "out" of the boundaries of...
2. ### Rectilinear movement seen from a rotating reference frame

Let's suppose there's some platform that is rotating with angular speed omega and has a radius R. At t=0 we release some object from the border, which has an initial speed perpendicular to the radius direction with magnitude \omega R and we want to know its position at t=T with respect to the...
3. ### 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...
4. ### I Galilean spacetime as a fiber bundle

Hi, reading the book "The Road to Reality" by Roger Penrose I was a bit confused about the notion of Galilean spacetime as fiber bundle (section 17.2). As explained there, each fiber over absolute time ##t## is a copy of ##\mathbf E^3## (an instance of it over each ##t##), there exist no...
5. ### I Equivalence principle

Einstein's equivalence principle states that: The sets of inertial frames in the real world that correspond to (portions of) the ideal set of inertial frames discussed in special relativity consist of freely falling local frames. In other words,can we say that since all the local frames are in...
6. ### Natural frequency in stationary and rotating frames...

Hi, I am trying to gain insight into using stationary vs. rotating coordinate frames for natural frequency calculations. I have seen many FE codes suggest that critical frequencies can be calculated differently in rotating and inertial frames, so i wanted to do a 1D calc to see for myself how...
7. ### I The rising railway coach

You are launched upward inside a railway coach in a horizontal position with respect to the surface of Earth, as shown in the figure. After the launch, but while the coach is still rising, you release two ball bearings at opposite ends of the train and at rest with respect to the train. a)...
8. ### Inertial Reference Frame Proof

Consider a specific reference frame (0XYZ) attached to Earth. A point (origin) being selected, coordinates are ascribed along with a vector basis. This reference is non-inertial because it is locked to Earth and the acceleration of Earth is not zero. Suppose upon rising one morning I felt...
9. R

### A The Lagrangian a function of 'v' only and proving v is constant

Hi everyone. So I'm going through Landau/Lifshitz book on Mechanics and I read through a topic on inertial frames. So, because we are in an inertial frame, the Lagrangian ends up only being a function of the magnitude of the velocity only (v2) Now my question to you is, how does one prove that...
10. ### Actuator on an accelerating body

Hello all, new member here. Signed up cause I am stumped by a physics problem. I am trying to size a linear actuator. Basically I have a large body that is accelerating at acceleration in x direction. I have a linear actuator aligned in the x direction that is rigidly attached to the large body...
11. ### Frames of Reference: Linear Acceleration View - Comments

kuruman submitted a new PF Insights post Frames of Reference: Linear Acceleration View Continue reading the Original PF Insights Post.
12. ### Need for Lorentz transformation in pre-relativity period

What was the need for Lorentz transformation in pre-relativity period? Why was it necessary for the velocity of light to be invariant between different inertial frames and hence what was the need for Lorentz transformation when it was believed that velocity of light was constant with respect to...
13. ### I Special relativity and inertial frames

What in the mathematics of the derivation of special relativity limits the model to inertial frames? How is an inertial frame defined in the context of the derivation?

Definitions: Astronaut is A Person on Earth is B A travels to a star far away at near light speed, A would see B's time dilate. B would also see A's time dilate Twin paradox revived: What would happen if A returns to B at a very slow speed? Then both frames of reference would see each others'...
15. ### B Help Understanding special relativity

I'm trying to understand something about relativity that doesn't seem to add up. I will extend Einstein's carriage example to incorporate 4 clocks. At the beginning all these clocks are running at the same time when they are together. I put two of the clocks far away from each other (100 km...
16. ### Coriolis force and conservation of angular momentum

I'm trying to understand the relations between the existance of Coriolis force and the conservation of angular momentum. I found this explanation on Morin. I do not understand the two highlighted parts. In particular it seems that Coriolis force is there to change the angular momentum of the...
17. ### Is polar coordinate system non inertial?

Studying the acceleration expressed in polar coordinates I came up with this doubt: is this frame to be considered inertial or non inertial? (\ddot r - r\dot{\varphi}^2)\hat{\mathbf r} + (2\dot r \dot\varphi+r\ddot{\varphi}) \hat{\boldsymbol{\varphi}} (1) I do not understand what is the...
18. ### Frames of reference

is space an inertial or non inertial frame of reference?
19. ### How to check if frame is inertial?

inertial frame is one in which isolated particle has constant velocity but is there actually any "isolated particle " ? how then can frame be defined as or not being inertial ? or is it that - for a system in which acceleration due to external forces is equal for all members , the frame of...
20. ### Torque on a fixed reference of falling masses

I had a little thought experiment, in which there are two objects with the same masses near each other (same height) on freefall. If I set up a point that is on an instant besides the two masses and call it the center of torque, I get that the torque produced by the nearest one's weight is...
21. ### Trouble with definition of Newton's First Law

The lecturer in my dynamics class defined Newton's First Law to be 'There exists at least one inertial frame with respect to which mass m moves in a straight line with a constant velocity. In this frame no net force acts on m.' This has confused me; I thought inertial frames could not...
22. ### Galilean Relativity and Newton's Laws

I'm a little bit confused about the relationship between Galileo's Principle of Relativity and Newton's Laws. Indeed, as I understand, the Galilean Principle of Relativity is what Galileo presented with Salviatti's ship discussion. The discussion seems to lead to a simple idea: "if one performs...
23. ### Euler Angle from Body Frame to Inertial Frame

Hi, This is not really a homework problem, but a project I'm working on. So, I am trying to build a Simulink model for my quadcopter. I derived the equations of motion using the Newtown-Euler method in the body frame to get transnational and angular acceleration. For the transnational part, I...
24. ### Direction cosine matrix of rolling disk on circular ring

Hey all, I'm stuck on this problem and not sure how to proceed/if I'm in the right direction. Problem: One reference frame N sits at the origin (inertial frame) while another frame, B, describes a disk rolling on a circular ring about the other frame. Picture below (A) find the direction...
25. ### Diffraction wavelength of particles in moving frames?

Here's a question I cannot seem to comply with my understanding of Quantum Mechanics. The characteristic wavelength of a particle is responsible for diffraction interference fringes, which is part of the wavefunction solution to the schrodinger equation. But the wavelength of a particle is...
26. ### Was Einstein lucky when not considering twin paradox as paradox?

hi, Einstein did not even consider the twin paradox as problematic at all, he argued that it is a simple consequence of his special relativity? obviously he never gave a explanation of why the two twins don't age the same he instead left it to others to do so. was Einstein just having a hunch...