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. parshyaa

    Question about inertial and non inertial frames

    Suppose a person A is standing in a bus and bus is accelerating forward then when a person B standing outside observes A he see that A is accelerating in forward direction then there must be a force acting on him which is making him accelarating(because Newtons first law holds in Earth's frame)...
  2. 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...
  3. 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...
  4. T

    B Electric+Magnetic Force Between a & b Charges: Inertial Frames

    Let's assume that a and b charges are moving. now in our lab frame there will be a electric+magnetic force whereas in a rest frame of either of the charges, there will be only an electric force. So, two inertial observers will measure different forces?
  5. 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...
  6. T

    I How to prove gravitational mass & inertial mass equivalence?

    There is a video on YouTube where Sean Carroll says for Newton it was just an accident that inertial mass equals gravitational mass, but with the general theory of relativity it became obvious that it has to be so. How does one see that? My own attempt has been consisting of transforming...
  7. R

    Who is Dr. Robert, a Multifaceted Scientist and Educator?

    I am a Rutgers and NJIT-educated professor of Physics, now under contract to Farmingdale State College and Nassau Community College, with other recent assignments at LIU Post and the BOCES Regional STEM High School. I embarked on doctoral-level studies in 2010 at Stony Brook University in their...
  8. Pushoam

    I Laws of physics and inertial systems

    It is not the laws of physics, but the forms of laws of physics which are the same in all inertial frames. Comment."The forms of laws of physics are the same in all inertial frames" is a necessary condition (put by scientists ) to get satisfied by something which has to be called as a law of...
  9. N

    Is Charge Equivalent to Inertial Mass?

    I've read about the equivalence between inertial mass and gravitational mass. But i can't undestand why is gravity more special then other kinds of force. I mean, why isn't charge equivalent to inertial mass? After all charge plays the same kind of role of gravitational mass in another context.
  10. C

    A Inertial Frames: GR to SR | General Relativity

    Hello everyone, here I come with a question about inertial frames as defined in General Relativity, and how to prove that the general definition is consistent with the particular case of Special Relativity. So to contextualize, I have found that one can define inertial frames in General...
  11. 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...
  12. T

    Calculating inertial moment of a disk

    Hi, I have a disk of diameter r, and the mass of the disk is 1kg. I'm going to rotate the disk at its center. my question is: 1. let's say I put a load of m kg on top of the disk, does the moment inertia of the system is as simple as (m + 1kg)r2/2? 2. does the shape of the load put on top of...
  13. 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?
  14. Ontophobe

    Inertial Privilege: Reframing Physics for Accelerated Frames

    There are inertial reference frames and accelerated reference frames, and the laws of physics change depending on the frame through which you're observing them. The universe when viewed through an inertial frame won't let you go faster than light, but the very same universe when viewed through...
  15. Wout Veltman

    I Kinetic Energy & Speed in Inertial Frames: Chris, Bob & Angelica

    From Chris' perspective Bob is traveling with 1.5*108 m/s in direction a. Angelica is also traveling with 2.4*108 m/s in direction a. From Bob's perspective Chris is traveling with 1.5*108 m/s in direction b (The opposite of x). Angelica is traveling with 1.5*108 m/s in direction a. They all...
  16. 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...
  17. Aler93

    Particle´s acceleration respect two inertial frames

    Homework Statement System S' moves with constant speed v=(vx,0,0) respect to the system S. On the S' system a particle moves with a constant acceleration a=(ax,ay,az). What is the acceleration a'=(ax',ay',az') measured from the system S?. Homework Equations Lorentz transformation The Attempt...
  18. J

    Momentum and Inertial Reference Frame

    Homework Statement At the roller rink, two 20-kg girls accelerate toward each other until they are each moving at 2.7 m/sin the Earth reference frame. They then collide stomach-to-stomach, grab on to each other, and fall to the floor. A. Calculate the magnitudes of the momentum of each girl...
  19. O

    Rotational motion with inertial forces

    Homework Statement Homework Equations Centripetal acceleration$$=\omega ^2R$$ Coriolis acceleration $$=2v_{rot}\omega $$ The Attempt at a Solution [/B] Think of the mass as lying on an incline. The forces I know are parallel to the incline are $$mgsin(\alpha), \mu N$$ Forces I know are...
  20. 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...
  21. 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...
  22. W

    Moving rod viewed in different inertial frames

    Homework Statement Two inertial frames S and S' are in standard configuration, the frame S' is moving along the x-axis of S with velocity v. In S' a straight rod parallel to the x' axis moves in the y' direction with velocity u. Show that in S the rod is inclined to the x-axis at an angle ##-...
  23. powerof

    I Curl from requiring invariance under inertial coordinate changes

    While investigating about the curl I have found this interesting perspective: http://mathoverflow.net/a/21908/69479 I lack the knowledge to do the derivation on my own so I would like to ask for your help. I am an undergraduate. I do not understand what a "first order differential operator"...
  24. E

    Solving this question from an inertial FOF

    Homework Statement Need to find the time t taken for m to reach the bottom Homework Equations F = ma The Attempt at a Solution [/B] I don't know how to go about solving this from an inertial frame. In my view, the only two forces acting on this block are mg, which has a mgsin(theta)...
  25. S

    Coriolis effect causes in motion of a free falling object

    I don't understand what are the causes of the Coriolis effect for objects moving with respect to Earth. For istance consider an object free falling on the Earth from an height h. Its tangential velocity its greater than the velocity of an object on the surface of Earth, hence it moves eastward...
  26. H

    Inertial tensor remains diagonal during a shift along a principle axis

    In the middle of the below paragraph: "only if the shift vector ##R## is along one of the principal axes relative to the center of mass will the difference tensor be diagonal in that system." I suppose the difference tensor means new inertial tensor ##-## old inertial tensor. That means the new...
  27. SophiaSimon

    Classical Mechanics: Inertial Reference Frames

    Homework Statement Classical Mechanics: John Taylor[/B] (1.27) The hallmark of an inertial reference frame is that any object which is subject to a zero net force will travel in a straight line at a constant speed. To illustrate this, consider the following experiment: I am standing on the...
  28. M

    I Solving Determination of Locally Inertial Coordinates

    Hello, I am studying on my own from Weinberg's Gravitation and Cosmology and I cannot understand how he derives a solution (pg. 72). I did not know where else to post this thread since it is not homework exercise. He takes a coordinate system ## \xi^a## "in which the equation of motion of a...
  29. 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...
  30. pixel

    I Earth as Inertial Ref. Frame: Test Relativity's Precision

    Special relativity is one of the most tested theories in physics. A central postulated of SR is that the speed of light is the same for all observers in inertial reference frames, and this leads to time dilation and the other effects that have been tested with a high degree of precision. We...
  31. B

    B Distinguishing inertial reference frames

    As described in Wikipedia as well as this entry http://physics.stackexchange.com/questions/172739/is-the-lay-explanation-of-the-equivalence-principle-wrong, "being at rest on the surface of the Earth is equivalent to being inside a spaceship (far from any sources of gravity) that is being...
  32. 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?
  33. 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...
  34. H

    Correction term while switching from inertial to body fixed

    Suppose we have an equation in inertial frame A. \begin{equation}\frac{{}^Ad\bf{H}_C}{dt} = \bf{M}_C\end{equation} Now we want to switch to body fixed frame B. For this need to employ correction factor {}^A\bf\omega^B\times\bf{H}_B. Why do we have this correction factor? How to derive this...
  35. N

    Quantifying Inertial Resistance

    Hi! I am having a little trouble with a question asked by a colleague. There’s a ball B with a certain mass M, at rest. A small ball A of mass m is moving with speed v toward M. If m=M, and the collision is perfectly elastic and the two objects perfectly rigid, than we know that A would come...
  36. C

    I Twin Paradox Resolution -- Inertial frames

    Thinking and reading about the twin paradox recently, I encounter a lot of explanations and resolutions that don't make sense to me. At its most basic, the issue is- when two bodies are in different frames of reference, why shouldn't relativistic effects affect both equally, negating time...
  37. B

    Diagonal of a thin rectangular foil, inertial principal axis

    I'd like to know if the diagonal of a rectangular thin foil is an inertial principal axis.I know that if an axis isn't a symmetry axis then it isn't a principal axis. In the rectangle the diagonal isn't a symmetry axis, so it shouldn't be a principal axis. Is it correct? So, if I consider that...
  38. B

    Acceleration in a non inertial reference frame

    Homework Statement A platform rotates with ##\omega=10## rad/s around ##z##-axes. A ball is connected, with a yarn to ##z##. Its distance to the axes is 15 cm and it rotates with ##\omega=10## rad/s. There isn't friction between platform and ball. Suddenly, the angular velocity of the...
  39. C

    Conceptual difference between gravitational and inertial mas

    I know that this question has been asked many times before on this forum, but on every existing thread either the question or the answers, or both, were too vague. I understand that inertial mass is defined as the property of an object to resist change of its velocity, that is the mass that...
  40. A

    How a rotational motion could be in an inertial ref. frame

    When rotation exists, so does the radial acceleration. It can be defined as ar=-ω2xr So there is a kind of acceleration with rotation all the time. Thus, we have to use non-inertial reference frame all the time. Could a rotational movement be analysed in an inertial ref. frame?
  41. AHashemi

    Direction of (Inertial) centrifugal force here?

    Homework Statement an object is sliding on an elliptical hill shown in picture. what is the direction of (inertial) centrifugal force at each moment? Homework Equations F=mv^2/r The Attempt at a Solution I think it should be towards the center of ellipse and value of r in the formula varies...
  42. T

    What is the effect of heat on the inertial mass of a body?

    I mean, a body with higher temperature has higher energy so is it heavier than before? We know from e=m*c^2 that energy is equivalent to mass
  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. Geofleur

    Momentarily co-moving inertial frames

    I wanted to check my understanding of momentarily co-moving inertial frames, so I came up with this example: Consider an inertial frame (with unprimed coordinates), about whose origin a clock moves in a circular path with constant speed, ## v ##. What is the time elapsed on the moving clock...
  45. 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.
  46. J

    Inertial forces of a slider crank

    Homework Statement Hello, I have an exam later in the week and I'm trying to understand how to this problem. Homework Equations Sum of forces. Sum of moments. The Attempt at a Solution I broke the mechanism into 3 pieces, the crank, connecting rod, and slider and then began to analyze...
  47. R

    Convert ECI to ECEF: A Step-By-Step Guide

    I have done a search online to understand how to convert ECI to ECEF. I wanted to learn what the conversion is so I could just create a MATLAB script to make it happen. My problem is that most of the information I find assumes you already have some knowledge about ECI and ECEF. If I had more...
  48. T S Bailey

    Inertial observers explanation for unruh thermalization

    Imagine two observers, one accelerating and one inertial. The accelerating observer detects a thermal bath whereas the inertial observer detects a vacuum. I would imagine that this hot gas would thermalize the accelerating observers spaceship, but how does the inertial observer reconcile this...
  49. 0

    Invariance of Acceleration in Inertial Reference Frames

    Claim: The acceleration (both direction and magnitude) for any object is the same in any inertial reference frame. Is this claim true? I think it is, but someone mentioned to me that time may be an issue as it's not agreed upon in all inertial reference frames. I'd appreciate any references...
  50. E

    How rockets take curved paths in space (absent gravity)

    This might have been answered before but it's something that has been bothering me. A rocket in space will move in a straight line. If I apply thrust, it still moves in a straight line unless I apply the thrust in a different direction. So unless I have rocket nozzles attached to the side...
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