# What is Reference frame: Definition and 229 Discussions

In physics, a frame of reference (or reference frame) consists of an abstract coordinate system and the set of physical reference points that uniquely fix (locate and orient) the coordinate system and standardize measurements within that frame.
For n dimensions, n + 1 reference points are sufficient to fully define a reference frame. Using rectangular (Cartesian) coordinates, a reference frame may be defined with a reference point at the origin and a reference point at one unit distance along each of the n coordinate axes.
In Einsteinian relativity, reference frames are used to specify the relationship between a moving observer and the phenomenon or phenomena under observation. In this context, the phrase often becomes "observational frame of reference" (or "observational reference frame"), which implies that the observer is at rest in the frame, although not necessarily located at its origin. A relativistic reference frame includes (or implies) the coordinate time, which does not equate across different frames moving relatively to each other. The situation thus differs from Galilean relativity, where all possible coordinate times are essentially equivalent.

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14. ### B Fluid Continuity Equation in different reference frame

If I have fluid with area 10 and velocity 10, if the velocity increases to 20 the area will become 5. But if we switch to a reference frame moving at velocity 1 opposite this motion, then it would be 10 and 11 to 5 and 21, violating the continuity equation. What is wrong?
15. ### Is this a reference frame problem ?

v1 - velocity of the rain with respect to the ground v2 - velocity of the man with respect to the ground v3 - velocity of the rain with respect to the man So, v1 = v3 + v2 is this right ? So, for the man moving with a velocity v2 with respect to the ground, the rain will have a horizontal...
16. ### I Reference Frame, Difference in Kinetic Energy, Fuel Consumed

Say 2 cars are traveling side by side at 10 m/s in some flat, wide open space. Relative to each other they are stationary. Relative to someone on the ground they are both moving at 10 m/s. Now say you're in 1 of the cars and you see the other car accelerate, changing his velocity by 10 m/s in...
17. ### I Synchronous Reference Frame: Definition and Usage

Hi, reading the Landau book 'The Classical theory of Field - vol 2' a doubt arised to me about the definition of synchronous reference system (a.k.a. synchronous coordinate chart). Consider a generic spacetime endowed with a metric ##g_{ab}## and take the (unique) covariant derivative operator...
18. ### Simple conceptual reference frame question

If a train is moving at some constant V with a bed sitting still on top. When the train decelerates at some rate -A then the bed will move at some acceleration A. I can't seem to get an intuition for how this comes to be. I have looked online and find no help.
19. ### I Does the CMB reference frame violate the Cosmological Principle?

Studies of the Cosmic Microwave Background shows that the Earth is moving roughly 380 km/s with respect to it towards the constellation Leo I think. Yet (I think) the Cosmological Principle and the Michelson-Morely experiments suggest there is no preferred reference frame in the universe --...

21. ### Body-Fixed Reference Frame -- How is it useful?

Hello Everyone, I am trying to understand the usefulness of a body-fixed (body-centered) frame of reference ##O'x'y'z'## versus a lab frame of reference ##Oxyz##. The body-fixed frame is attached to the moving body and changes orientation exactly as the body changes orientation. From the...
22. ### Reference frame in collision problems

2 balls (Ball 1 and Ball 2) collide fully elastically and their relative velocity stays the same as but in sign opposite to that before the collision. Is there any sort of reference frame in which Ball 2 is always fixed (at rest) so that one can look at their relative velocity always in that...
23. ### I Reference frame vs coordinate chart

Hello, here on PF I've seen many threads about the concepts of 'reference frame' and 'coordinate system'. In the context of SR my 'envision' about the concept of 'frame of reference' is basically the 'rods & clocks latticework' as introduced in the book Spacetime physics (Taylor, Wheeler)...
24. ### Equations of relative motion with respect to a rotating reference frame

Hi, I am just writing a post to follow up on a previous thread I made which I don't think was very clear. The question is mainly about how to use the below equations when there is also a rotation of the body around the fixed reference point. Please see the diagram here to see how the vectors...
25. ### I Momentary Co-Moving Reference Frame in SR

In SR, for the momentary co-moving reference frame, U (the velocity four vector) takes the form (1,0,0,0). I'm wondering whether the basis vectors associated with this velocity are zero or if the coefficients in front of the basis vectors are zero. In classical mechanics we would say that the...
26. ### Question about Formulae for Motion in a Rotating Reference Frame

Hi, I am reading the following question: "Particle P moves in a circular groove with radius ## a ## which has been cut into a square plate with sides of length ## l ##. The plate rotates about its corner ## O ## with with angular velocity ## \omega \hat k ## and angular acceleration ## \dot...
27. ### B Earth Center of Mass: GR & Inertial Object Acceleration

Super-basic question that I'm embarrassed to ask. It's just what the summary says: Taking Earth's center of mass as our reference frame, how does GR account for an inertial object near the surface approaching with an acceleration of G? I assume (perhaps incorrectly) that this is an inertial...
28. ### I The reference frame for angular momentum components

In which coordinate system the components of angular momentum are quantized? Better to say, if we can select the coordinate system arbitrarily, how the components of angular momentum, say z-component, are always ##L_z=m\hbar##?
29. ### 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...
30. ### B Time dilation and the reference frame of the vacuum

The point of the twin paradox in special relativity is that the traveling twin experiences a real, frame-invariant effect in which the time evolution of all moving matter is slowed down. If you read a hundred articles and textbooks on SR, you'll see a hundred variations on the message that the...
31. ### A Reference frame of the vacuum -- which forum?

I have a question about interactions between matter and the vacuum, but I don't see a forum for that. Quantum field theory seems to be the most closely related subject. What would be the best forum for questions related to QFT?
32. ### I Comoving Reference Frame in Cosmology

In cosmology, the preferred reference frame is the comoving rest frame. I am trying to understand why we are using this frame and not another one. The only reason I could come with is this. Since the expansion of the universe is homogeneous and isotropic it seems our best choice is using the...
33. ### I Does Conservation of Momentum & Energy Hold in the C.O.M. Reference Frame?

We know classical equations fail to follow conservation of momentum and energy when we are dealing with speeds closer to the speed of light. But does it fail in the center of mass reference frame of a system?
34. ### 1st Law of thermodynamics : moving reference frame

I'd like to apply the 1st law of thermodynamics in a reference frame (RF) moving with constant velocity. We have: ##\Delta{}E = E_{in} - E_{out}## I am limiting myself to rectilinear motion. Suppose we are in a RF moving with a constant velocity ##V##. Let the system consist of a mass ##m##. The...
35. ### B Length Contraction in Accelerated Frame

I was wondering, would there be a length contraction (or expansion) in the z and y axis' if an object was accelerating in x axis? I know that in special relativity there is no deformation in the y and z axis' if the object is moving in the x axis. I was looking a this paper for clarification.
36. ### Acceleration for a non-inertial reference frame

Well, first a wrote the equation for acceleration in non inertial systems. ##a_I=a_o+\dot \omega \times r+\omega \times (\omega \times r)+2(\omega \times v_{rel}) +a_{rel}##. Then, ##a_o=0## (because the system doesn't move), ##a_i=0## (because it is measured from the non inertial system)...
37. ### Acceleration in special relativity

I'm struggling in the details of this exercise. Let ##S'## be the reference frame where the acceleration of the spaceship is constant, in which case we have ##u'(t')= a' t'## (since we assume no acceleration at the beginning). The rest frame of the rocket ##S## is connected to ##S'## via a...
38. ### 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...
39. ### Measuring position and velocity from a non inertial reference frame

I) For ##A##, the positition is ##\vec r=(0;V_0 . t;0)##. For ##B##, we have ##\vec r_A=\vec r_B + \vec r_{A/B}##, but ##\vec r_{A/B}## is equal to zero because they have the same origin, so the position measured from ##A## is equal to the position measured from ##B## II) For ##A##, velocity...
40. ### Entropy in a non inertial reference frame

I know that the entropy of a system is the same in different inertial frames. Is this still the case for non inertial frames? For example, is the entropy of a body as seen from a rotating reference frame the same as the entropy seen from a fixed frame?
41. ### B Reference frame symmetry in Special Relativity

Hello, I have a couple of questions related to reference frames in Special Relativity. Let's consider a rocket that is inertially moving towards a star with a relative velocity 0.9c. I'd like to look at this example from both the rocket's and the star's perspectives. In the reference frame of...
42. ### B Attribution of Reference Frame: A Dilettante's Question

I can't find an answer on my dilettante question about how we attribute reference frame to complex objects, where different parts move with different velocity or where different parts experience different influence of gravitation. For example, we can take a human's body. If we take the full...
43. ### A Can an object be at rest in its own reference frame?

In classical physics, every object is obviously at rest with itself, and it makes perfect sense for this to be true. But would this violate the uncertainty principle for a particle? If you are the particle and you know that you're at rest with respect to yourself, you know both your location...
44. ### Solving for c: Speed of Q2 in Q1 Reference Frame

I've tried using this equation: Where: u' = 0.86c v = 0.3c u = Is the speed of Q2 as measured by an observer in the reference frame of Q1 = 0.922c Where have I gone wrong? Have I missed a negative symbol?
45. ### B Polarized Electron in a Rotating Reference Frame

I tried asking a similar question in cosmology but got no answer there so here goes... Suppose I am on a windowless spacecraft in the middle of an intergalactic void. I know that the spacecraft is spinning from measuring the centrifugal forces but have no way of observing the outside...
46. ### Angular momentum of a system relative to a moving reference frame.

I don't have too much of a clue of how to begin the problem. I first wrote the angular moementum of the system of particles: →M=∑mi(→ri×→vi)M→=∑mi(r→i×v→i). Then I know that the angular momentum from of the moving reference frame would have the velocity as the sum of the velocity of the frame...
47. ### I Locally inertial reference frame problem

Hey PF, I am working on a problem set, and one of the problems is proving that the Christoffel symbols vanish at the origin of the coordinates ##y^{\alpha}## given by the coordinate transformation: y^\alpha (x) = x^\alpha - x^\alpha_{(0)} + \frac {1} {2} (x^\mu - x^\mu_{(0)} )(x^\nu -...
48. ### Rotating Reference Frame

I have a ball of mass m that is situated on horizontal plane on the northern Hampshire. I am asked to show that the ball is moving, clockwise, in a manner of r = v / ( 2Ω*sin(λ) ) where v is the ball's velocity, Ω is Earth's angular velocity, and λ is the terrestrial latitude So here's what...
49. ### A Reference frame conversion for a moving sphere

Hi here is the situation; There's a spherical particle contained with a MEMS sensor (3D accelerometer and gyroscope) moving down a bed. What we want is to estimate the total kinetic energy of the particle. The total kinetic energy has two parts, translational part and rotational part. for the...
50. ### Position of particle in inertial reference frame

Homework Statement The position of a participle in a fixed inertial frame of reference is given by the vector r = i(x0 + Rcos(Ωt)) +j(Rsin(Ωt))where x0, R and Ω are constants. a) Show that the particle moves in a circle with constant speed Homework Equations F = mv2/r The Attempt at a...