Non-inertial frame Definition and 54 Threads

A non-inertial reference frame is a frame of reference that undergoes acceleration with respect to an inertial frame. An accelerometer at rest in a non-inertial frame will, in general, detect a non-zero acceleration. While the laws of motion are the same in all inertial frames, in non-inertial frames, they vary from frame to frame depending on the acceleration.In classical mechanics it is often possible to explain the motion of bodies in non-inertial reference frames by introducing additional fictitious forces (also called inertial forces, pseudo-forces and d'Alembert forces) to Newton's second law. Common examples of this include the Coriolis force and the centrifugal force. In general, the expression for any fictitious force can be derived from the acceleration of the non-inertial frame. As stated by Goodman and Warner, "One might say that F = ma holds in any coordinate system provided the term 'force' is redefined to include the so-called 'reversed effective forces' or 'inertia forces'."In the theory of general relativity, the curvature of spacetime causes frames to be locally inertial, but globally non-inertial. Due to the non-Euclidean geometry of curved space-time, there are no global inertial reference frames in general relativity. More specifically, the fictitious force which appears in general relativity is the force of gravity.

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  1. B

    I Earth's angular velocity when axis is aligned with apparent gravity

    I've been reading the book "Classical Mechanics" by John Taylor, and in the chapter about noninertial reference frames, it states that the direction of 𝑔 (the apparent gravity, which includes the centrifugal force) is not necessarily aligned with the direction of 𝑔0 (the true gravity direction...
  2. tracker890 Source h

    Q2: In a relative non-inertial reference frame, why is fluid velocity zero?

    Q： Referring to the solution of this problem, why does the equation (eq) hold true? $$ \frac{\partial}{\partial t}\int_{CV}^{}{u_{xyz}}\rho d\forall =\frac{\partial}{\partial t}\left( u_{xyz}\cdot M \right) =M\left( \frac{\partial}{\partial t}u_{xyz} \right) =M\left( \frac{\partial}{\partial...
  3. tracker890 Source h

    Q: In a relative non-inertial reference frame, the fluid velocity is zero?

    Q： Regarding item (4), my understanding aligns with (eq_1), where M is a constant. However, why does ##\left( \frac{\partial}{\partial t}u_{xyz} \right)## in (eq_1) equal 0? $$ \frac{\partial}{\partial t}\int_{CV}^{}{u_{xyz}}\rho d\forall =\frac{\partial}{\partial t}\left( u_{xyz}\cdot M...
  4. G

    I Inertia/Non-inertial frame - isotropy

    It's known that in inertial frame, space is isotropic. (statement of this where I have taken out of is attached as image) When we talk about an uniform accelerated train, ground frame is considered as inertial frame(at least in newtonian mechanics). So if ground frame is considered such as...
  5. V

    I Non-Newtonian description of an accelerated object

    Hello, everyone! In the first few chapters of Physics 1, there is the description of motion, and the computation of the acceleration vector as being the sum of the rate of change of velocity, with the division of linear velocity squared by the instant radius of curvature: The above equation...
  6. L

    I Galilean transformation of non-inertial frame

    It's frequently discussed Galilean transformation brings one inertial frame to another inertial frame, and such a transformation leaves Newton's second law invariant (of the same form). I wonder what happens for non-inertial frame? If we start with a non-inertial frame, and Galilean transform...
  7. Z

    Possible to use work-energy theorem from a non-inertial frame?

    In learning about translational and rotational motion, I solved a problem involving a wheel rolling down an inclined plane without slipping. There are multiple ways to solve this problem, but I want to focus on solutions using energy. Now to my questions. The reference frame in the posted...
  8. MD LAT 1492

    I Relative Motion & Local Frame’s Position - when projecting components

    Does the position of the origin for the body’s rotating coordinate frame 1) stay fixed to the moving body or 2) does it stay fixed to the inertial frame, yet still able to rotate as the body rotates with the only restriction that it cannot translate with the body i.e. only affixed at the...
  9. F

    Whether a non-inertial frame is absolute

    If a frame is a non inertial frame, then it must have an acceleration. Then which reference frame is this acceleration with respect to? If this acceleration varies with the reference frame this acceleration is calculated with respect to, is this non inertial frame absolute?
  10. X

    Is Coulomb's law valid in a non-inertial frame?

    Hi, I was wondering, if the charges do not move in a non inertial frame and I don't move too in this frame, will I see the same Coulomb force, some fictitious forces and radiation coming from these static charges? Thanks!
  11. A

    Can Mechanical Energy Be Conserved in an Accelerated Frame?

    In the frame of the accelerated block, I applied the non-inertial force F'. My doubt is if I can conserve the mechanical energy in the accelerated frame and find the speed at the top. Otherwise, how could you proceed.
  12. 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...
  13. Leo Liu

    Is angular momentum conserved in a non-inertial frame?

    Question: If we place the frame of reference on an accelerating point, does the total rotational momentum still remain the same? I attempted to solve this question by manipulating the equations as shown below. $$\text{Define that }\vec r_i=\vec R+\vec r_i'\text{, where r is the position vector...
  14. 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...
  15. cianfa72

    I Speed of Light in Vacuum in Non-Inertial Frame

    Hi, I read various threads in PF about the concept of invariant speed and the speed of light in vacuum that in our universe happens to be the same as the 'invariant speed'. My doubt is about the speed of the light in vacuum as measured from a non-inertial frame (basically in the context of SR...
  16. Like Tony Stark

    Acceleration acting on a block lying on a wedge (non-inertial frame)

    I have some difficulties trying to understand non-inertial frames. I have problems to notice the acceleration in these cases, from an inertial reference frame and from non inertial refrence frame. Consider the first case, if I'm on the wedge, I see that the block doesn't move so there's no...
  17. K

    Position formula in a non-inertial frame

    The equation ##x = x_0 + vt + at^2/2## is derived assuming a constant acceleration ##a##. My question is , from what frame is this path ##x(t)## described? Can I use it from a non inertial frame?
  18. L

    Effective acceleration due to gravity in non-inertial frame

    Take some sort of system accelerating with respect to an inertial reference frame: let's take a spherical mass on the end of a string forming a simple pendulum with the ceiling of a car, and allow that car to accelerate uniformly. Could someone share with me how they interpret the concept of a...
  19. G

    What are non-inertial frames of reference?

    I am reading through a textbook on AP Physics, and I came across a few references to non-inertial frames of reference. It doesn't clearly say what a non-inertial frame of reference is. Based on the examples it gives, I assume that it is a frame of reference where the observer is experiencing...
  20. C

    Forces in inertial and non-inertial frame of reference

    Imagine such situation: A bus is moving at constant speed, a man is standing on the bus and is not holding to anything - he is simply standing. Now, the bus starts breaking with constant negative acceleration and so the man will change his relative position due to the force of inertia. Now...
  21. Y

    Two masses connected by spring rotate around one axis

    Homework Statement Take the x-axis to be pointing perpendicularly upwards. Mass ##m_1## slides freely along the x-axis. Mass ##m_2## slides freely along the y-axis. The masses are connected by a spring, with spring constant ##k## and relaxed length ##l_0##. The whole system rotates with...
  22. S

    I Transformer Output in Non-inertial Frame: Frequency Change?

    In this example I'd like to know about the output of the transformer. What happens if an electromagnetic transformer is powered by a sine-wave and simultaneously accelerating at non-relativistic speeds? I assume the output will still be a sine-wave but the frequency will change. Is this correct?
  23. Andrea Vironda

    Motion in a non-inertial frame

    Hi, in this Landau's extract i note that the total derivative is neglected in 2 places. in the first case i think because it's raised twice, but in the second case?
  24. L

    "Shifting" non-inertial frame in Accelerating Atwood Machine

    Hello, I was referring to this thread: https://www.physicsforums.com/threads/accelerating-atwoods-machine-problem.44305/ to solve a problem on accelerating atwood machines in which, naturally, one attempts to find the acceleration of each of the individual masses. Although I now understand how...
  25. Pushoam

    How Does the Coriolis Effect Influence Falling Objects at the Equator?

    Homework Statement Because of the Coriolis force, falling objects on the Earth are deflected horizontally. For instance, a mass dropped from a tower lands to the east of a plumb line from the release point. In this example we shall calculate the deflection of a mass m dropped from a tower of...
  26. Pushoam

    Force on a bead due to a rotating wire

    Homework Statement A bead slides without friction on a horizontal rigid wire rotating at constant angular speed ω. The problem is to find the force exerted on the bead by the wire. Neglect gravity. Homework EquationsThe Attempt at a Solution The physical force acting on the bead is the force...
  27. F

    I Derivative of Lorentz factor and four-acceleration

    As far as I understand it, the Lorentz factor ##\gamma(\mathbf{v})## is constant when one transforms between two inertial reference frames, since the relative velocity ##\mathbf{v}## between them is constant. However, I'm slightly confused when one considers four acceleration. What is the...
  28. 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...
  29. parshyaa

    How earth is a non-inertial frame

    How (more accurately) Earth is a non inertial frame? A frame of reference(FOR) will be a non-inertial when a=0 ⇔ F =0 Suppose a book on a table is our object and Earth as a Frame of reference, generally we take accelaration of book w.r.t Earth as 0 but more accurately it is not 0(because...
  30. F

    Angular momentum is conserved, but KE is not. How to find out why?

    This (photo) is a very typical example of conservation of angular momentum, but my trouble arrises from trying to prove that the difference of energy will have to correspond to work, by calculating the work done by you to alter the moment of inertia. I have spent a lot of time in this, but I...
  31. P

    Trajectory of pendulum in frame of rotating disk under it

    Homework Statement Consider the pendulum depicted in the adjacent figure: a mass m is attached to non stretching chord of length `. Directly below the pendulum is a circular disc rotating with constant angular velocity w. We attach to the disk a frame whose x-axis is in the plane of the...
  32. J

    I Understanding Relativistically Spinning Disk/Ring: Lorentz Boosts

    I'm trying to understand the relativistically spinning disk within the framework of SR (if that is even possible). I thought to first simplify the problem by considering a spinning ring/annulus, but I don't know if my analysis is correct. I imagined a spinning ring of radius R, spinning at an...
  33. E

    B GR: Using Earth as a Reference Frame - Q&A

    I'm trying to get my head around GR. As I understand it, any frame of reference is as valid as any other for modeling the universe. Therefore, it is valid to use a non-rotating Earth as a frame of reference, and try to model the movement that is seen from this frame. But if that is true, I...
  34. F

    Acceleration due to fictitious force independent of mass?

    I have been asked by someone if it is true that in general, for a constantly accelerating reference frame, i.e. a non-inertial reference frame, the acceleration of a particle (as observed in this frame) due to the corresponding fictitious force is independent of its mass. My response was yes...
  35. B

    Explanation for Non-Inertial Frames of Reference

    Homework Statement Why do objects that have no external net force acting on them accelerate? Ex. If a ball is on an accelerating train, it will accelerate opposite the direction of the train's acceleration, assuming there is nothing blocking its path of motion and it is not strapped down. My...
  36. B

    Non-inertial Frames of Reference

    Homework Statement You are in a car accelerating forwards. There is a baseball at your feet. Draw two FBDs showing the the ball's motion from the frame of reference of the car and the frame of reference of the sidewalk. Which frame of reference is non-inertial? In which frame do you observe the...
  37. B

    Frames of Reference: Inertial vs Non-Inertial

    is space an inertial or non inertial frame of reference?
  38. R

    Non-inertial frame of reference

    Homework Statement You use a string to suspend a cork ball with a mass of 22.0g from the ceiling of a moving speedboat. The ball and string hang at 32.5 degrees from the vertical. Calculate the acceleration of the speedboat.Homework EquationsThe Attempt at a Solution I was able to calculate...
  39. H

    Centripetal Force: Inertial vs Non-Inertial Frame Time

    Hello, I've been thinking about inertial and non inertial reference frames. A common example is non rotating reference frame vs a rotating reference frame. As illustration, I have attached two images below. The left is the inertial frame and the right is the non inertial frame. Both...
  40. M

    Non-Inertial Frame: Key Clues & Examples

    I confuse when should I use non-inertial frame... is there any keyword or key clues that remind you of using non-inertial frame of reference? can anyone help explain this with an example?
  41. J

    Measurement of relativistic effects from a non-inertial frame

    I was just thinking about this, and from a perspective of an inertial frame, it's easy to see how distances contract, times dilate, simultaneity varies between observer and the speed of light is exactly c in each case. But what about non-inertial frames? In the presence of gravity almost...
  42. sergiokapone

    Moving in an non-inertial frame

    Homework Statement In opposite points carousel diameter D = 20 m, rotating with constant angular acceleration, located at the point C shooter and target M. Shooter aiming at a target without introducing amendments to the rotation of the carousel. What should be the angular acceleration of...
  43. S

    Measuring an angle in non-inertial frame reference

    In class, we came up with an equation, a=gtanθ, to calculate the acceleration of a car using a hanging pendulum in Earth's frame of reference (θ being the angle that the pendulum makes with the vertical when the car accelerates). So far, I know that that the pendulum moves in the opposite...
  44. S

    Bead on a loop in a non-inertial frame

    Homework Statement Consider a bead of mass m on a loop of radius R. The loop is rotating at a constant rate ω. Using a non-inertial frames of reference, find all equilibrium points of the bead on the loop. Homework Equations \vec{F_e}=m\vec{a_r}...
  45. A

    How inertial frame of reference differs from non-inertial frame?

    We know that we can't say whether we are at rest or uniformly moving if we're in a einstein cage..but if the same medium is accelerating/decelerating can we being inside(and can't see outside) claim abt state of cage..?I ve read that a non-inertial can be converted to inertial by incorporating a...
  46. L

    Classical mech non-inertial frame bead on a rotating ring

    Homework Statement Consider the bead threaded on a cicular hoop of example 7.6 (pg 260), working in a frame that rotates with the hoop. find the equation of motion of the bead, and check that your result agrees with eq 7. 69. Using a free body diagram explain the result 7.71 for...
  47. L

    Lorentz transformation for non-inertial frame

    Are there lorentzian transformation equations relating non-inertial frame to inertial frame. Also are there transformations relating non-inertial frame to another non-inertial frame. By 'non-inertial frame', I mean frame of reference having absolute acceleration,jerk... or any n-th order time...
  48. S

    Inertial and non-inertial frame of reference

    Okay, so I know what inertial and non-inertial frames of reference are: 1. Inertial is when Newton's laws of motion hold. 2. Noninertial is when they do not hold (the object is accelerating without a force). And I have a few examples as well, such as when you are is in a car and the car is...
  49. J

    Major difference of Inertial and non-inertial frame of reference ?

    Major difference of Inertial and non-inertial frame of reference ?? What is the major difference or differences of Inertial and non-Inertial frame of reference?? Is it only: Inertial - Constant velocity, obeys the law of inertia Non-inertial - Acceleration, disobeys the law of inertia
  50. M

    A non-inertial frame is non-inertial with respect to what?

    Considerer a closed box into space: • In constant acceleration. • Turning around its axis. Einstein used the first case as a thought experiment (http://galileo.phys.virginia.edu/classes/252/mass_and_energy.html) that led to the general theory of relativity: the occupant of the box could...
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