What is Inertial frame: Definition and 127 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. cianfa72

    I Is time dilation a real effect?

    In the context of SR we know time dilation is basically the rate of change of moving clock's proper time w.r.t. the inertial frame coordinate time. It does mean that in principle the "tick events" of moving clock are compared against the time measurement of clocks Einstein's synchronizated in...
  2. 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?
  3. 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...
  4. 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...
  5. 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...
  6. 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...
  7. brotherbobby

    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...
  8. Livio Arshavin Leiva

    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...
  9. 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...
  10. 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...
  11. 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...
  12. cianfa72

    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...
  13. 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...
  14. 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...
  15. Buckethead

    B Time Dilation: Accelerating vs Inertial Frame

    This is probably common knowledge to relativity aficionados but at Example 7.3 in this paper: https://www.farmingdale.edu/faculty/peter-nolan/pdf/relativity/Ch07Rel.pdf I was surprised to read the author showing that a ship accelerating at 1g from rest for 1 hour and reaching a speed of...
  16. A

    What is and some explamples of inertial frame of reference ?

    I know this is a basic question, but I haven't understood deeply what a inertial frame of reference is, to be more specific, its relation with the first law of motion.
  17. Adam564

    Centipede inertial frame problem

    Homework Statement A high-speed centipede in S’ is 10.0 cm long measured at rest in S’. A butcher in S holds two cleavers (A and B) 9.00 cm apart (measured in S). The centipede runs at such high speed v across a chopping block that the butcher measures the length of the centipede to be 8.00 cm...
  18. P

    I Velocity of Particle vs Inertial Frame Velocity

    Hello all, This post is in reference to a previous homework post, found here: https://www.physicsforums.com/threads/show-that-f-gamma-3-ma.338744/ That thread is closed to further replies. Probably because it's nearly 10 years old. That thread is about deriving relativistic force from the...
  19. Jazzyrohan

    I Einstein's Equivalence Principle: Freely Falling Local Frames

    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...
  20. B

    I Inertial frame of freely falling body

    A freely falling body (falling in earth) accelerates with time. However, an object inside the body remains at rest (if it was initially at rest) or moves with a constant velocity if it was initially moving with constant velocity. In other words a frame fixed to the body is an inertial frame...
  21. S

    What is the force acting on a rotating body in a non-inertial frame?

    Hello! The angular velocity in the non-inertial frame of a rotating body of mass m is ##\Omega## and I need to find the force acting on the body (in the non-inertial frame associated with the body). In the book they say (without any derivation, they just state it) that the force is...
  22. T

    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...
  23. A

    Inertial frame where rods have same length

    Homework Statement I was re-reading my old Relativity book (by Rindler) and taking a look at some of the problems. He asks: Using a Minkowski diagram to establish the following result: Given two rods of rest lengths ##l_1## and ##l_2 (l_2 < l_1)##, moving along a common line with relativity...
  24. W

    I Answer: Understanding the Effect of Gravity on Falling Objects

    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)...
  25. parshyaa

    Question related to inertia and non inertial frame

    Suppose a person is standing in a bus, moving with constant velocity and then driver applied the breaks and the person standing moved forward as if something pushed him from behind Whats the reason behind this Is it because bus has become a non inertial frame and we have to add psuedo forces to...
  26. S

    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...
  27. T

    Is this point of contact an inertial frame?

    Consider a disc being pulled by a constant force F and it is performing pure rolling. Now, the disc has a certain acceleration, point A has a acceleration in right direction and another centripetal acceleration in vertically upward direction but it has zero instantaneous velocity because of pure...
  28. 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...
  29. arjunzv8

    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...
  30. kuruman

    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.
  31. CricK0es

    Calculating rest mass and energy (in an inertial frame)

    Homework Statement A particle is accelerated so it has a total energy of 10GeV measured in the accelerator’s rest frame. The particle's momentum is 8GeV/c in the same frame. Calculate... a.) Rest mass of the particle b.) Energy in an inertial frame in which its momentum is 6GeV/c c.) The speed...
  32. F

    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...
  33. redtree

    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?
  34. parshyaa

    Question based on non inertial frame of reference

    Suppose I am observing a object in a noninertial frame from a noninertial frame , then what will happen to the forces acting on a object with respect to both the frames, frame of reference (FOR) moving uniform with inertial FOR are themselves inertial frame , does it follow the same with a FOR...
  35. K

    I Time Dilation Between Astronaut A and Person B

    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'...
  36. H

    Inertial frame where plane waves have the same frequency

    Homework Statement Plane harmonic waves of 1/p, 1/q, 1/r and 1/s are travelling, respectively, in the directions of the (non-unit) vectors (1,1,1), (1,-1,-1), (-1,1,-1) and (-1,-1,1). Show that there exists an inertial coordinate system in which they have the same frequency if and only if...
  37. S

    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...
  38. T

    Non inertial frame of reference(rotating)

    Homework Statement $$g_o=\frac{GM}{R^2}e_R$$ where g0 is the gravitational acceleration, G = 6.67 * 10-11Nm2 /kg2 is the universal gravitational constant, M= 5.98 *1024 kg is the mass of the Earth, and R = 6.38 * 106 m its radius $$g = g_0-ω*[ω*(r+R)]$$....(8.29) where gravitational...
  39. S

    Coriolis force and conservation of angular momentum

    I'm trying to understand the relations between the existence 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...
  40. S

    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...
  41. P

    What's the difference between an inertial frame....

    And a cartesian axis system in physics? I thought about that and my answer is that a cartesian axis system is the same as a inertial frame of reference, is that true?
  42. hackhard

    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...
  43. N

    Local Inertial Frame in General Relativity - Neutrino

    Hello, in general relativity we introduce local inertial frames to be such frames where the laws of special relativity holds. Let ξα the coordinates in the local inertial frame, so we get ds²=ηαβdξαdξβ. If we switch the frame of reference to coordinates xμ : ξα=ξα(x0,x1,x2,x3) and with...
  44. M

    Inertial Frames of Reference - Understanding Special Relativity for 11-Year-Olds

    I'm 11 and I'm trying understand what Special Relativity is about. How many different inertial frames of reference do we have and what are they?? I know what it means.
  45. F

    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...
  46. G

    Understanding Inertial Frame of Reference

    There is a lot of discussion on this but I still have doubts. Can someone help clarify and point me to correct thread? Object free falls due to gravity (acceleration) so the frame should be non inertial for outside observer. But object does not experience pseudo force in free fall so it may be...
  47. Q

    If the speed of light is constant in any inertial frame

    If the speed of light is constant in any inertial frame then how do we measure a red shift or blue shift or why?
  48. O

    Inertial and non inertial frame of reference

    When I was surfing on a group in Facebook, I found two concepts very difficult to understand by reading the discussions in comments. Those concepts are inertial and non inertial frame of reference. Please make me understand these two concepts in simple words. Please don't suggest links as I...
  49. Rwindsor1

    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...