What is Fictitious forces: Definition and 37 Discussions

A fictitious force (also called a pseudo force, d'Alembert force, or inertial force) is a force that appears to act on a mass whose motion is described using a non-inertial frame of reference, such as an accelerating or rotating reference frame. An example is seen in a passenger vehicle that is accelerating in the forward direction – passengers perceive that they are acted upon by a force in the rearward direction pushing them back into their seats. An example in a rotating reference frame is the force that appears to push objects outwards towards the rim of a centrifuge. These apparent forces are examples of fictitious forces.
The fictitious force F is due to an object's inertia when the reference frame does not move inertially, and thus begins to accelerate relative to the free object. The fictitious force thus does not arise from any physical interaction between two objects, such as electromagnetism or contact forces, but rather from the acceleration a of the non-inertial reference frame itself, which from the viewpoint of the frame now appears to be an acceleration of the object instead, requiring a "force" to make this happen. As stated by Iro:
Such an additional force due to nonuniform relative motion of two reference frames is called a pseudo-force.
Assuming Newton's second law in the form F = ma, fictitious forces are always proportional to the mass m.
The fictitious force on an object arises as an imaginary influence, when the frame of reference used to describe the object's motion is accelerating compared to a non-accelerating frame. The fictitious force "explains," using Newton's mechanics, why an object does not follow Newton's laws and "floats freely" as if weightless. As a frame can accelerate in any arbitrary way, so can fictitious forces be as arbitrary (but only in direct response to the acceleration of the frame). However, four fictitious forces are defined for frames accelerated in commonly occurring ways: one caused by any relative acceleration of the origin in a straight line (rectilinear acceleration); two involving rotation: centrifugal force and Coriolis force; and a fourth, called the Euler force, caused by a variable rate of rotation, should that occur.
Gravitational force would also be a fictitious force based upon a field model in which particles distort spacetime due to their mass, such as general relativity.

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  1. chris25

    Fictitious forces on a rigid body

    I was confused by how to work this problem in a rotating frame. The solution read that the centrifugal force on the mass should be of magnitude 𝑚𝑤𝑅^2. However, I thought it would be 𝑚𝑤𝐿^2 where L is the distance between the mass and the center of the circle (L = l + R). What am I missing here?
  2. Z

    I Do Fictitious Forces Still Matter in General Relativity?

    hello it is well known that gravitationl force is actually a fictitious force generally speaking,are fictitious forces still necessary in general relativity ? the fictitious forces which we experience on a bus or on a car can also be understood as due to the spacetime distortion ?
  3. crudux_cruo

    B Confusion while trying to build intuition of centripetal force

    As I understand it, when a body undergoes uniform circular motion its velocity does not change in magnitude but instead direction. This change in velocity, or acceleration, is directed inward towards the center of the circle. If a body was not experiencing a net centripetal acceleration, then...
  4. P

    I Fictitious forces and their associated energies

    I understand the idea of a fictitious force. What I am confused about is the energy/potential associated with it. For example, if a cylinder of water is rotating, there apparently exists this centrifugal potential energy, which is obtained by integrating mrw^2 dr. Why is it that the...
  5. Hiero

    I Distinguishing gravity from fictitious forces

    Is the above statement accurate? I am just wondering, aren’t tidal forces also produced by the centrifugal force of a rotating frame? So then what really distinguishes gravity from fictitious forces? (I don’t know any general relativity so if you reference things like the Riemann curvature...
  6. E

    B Clarification of coordinate fictitious forces

    I was reading through this Wikipedia article and stumbled across a section related to outlining the differences between "state-of-motion" fictitious forces and "coordinate" fictitious forces. I have no idea what the second category is supposed to be, and wondered whether someone could explain...
  7. M

    B Measuring Fictitious Forces in a Closed Box

    I was reading the following article: https://en.wikipedia.org/wiki/Fictitious_force When I came across this passage: "This led Albert Einstein to wonder whether gravity was a fictitious force as well. He noted that a freefalling observer in a closed box would not be able to detect the force of...
  8. taalf

    Formula for fictitious moments

    Hi All, Everyone knows so called "fictitious" forces, also known as "inertial" forces. They are forces felt by some mass point placed in a non-inertial frame. For example: a ball in a moving car or in a carousel. Maybe most intuitive fictitious forces are centrifugal forces, but there are also...
  9. T

    I Fictitious forces -- name convention

    Hello all, I understand there are four d'Alembert (fictitious) (non-inertial) forces: 1. Coriolis 2. Centrifugal 3. Linear 4. Angular acceleration. But then I think about the Gyroscopic Effect (I understand how it arises, so that is not the issue). I am wondering if one can "classify" these...
  10. E

    Acceleration of Body in Elevator & Earth with 0.5g Rise

    Homework Statement A slope is inside an elevator. A body with the mass of m is on the slope. θ=30°. What would be the acceleration of the body in relative to the elevator if the elevator rises with an acceleration of 0.5g? What would be the acceleration of the body in relative to the Earth if...
  11. P

    Fictitious forces and artificial gravity

    I'd be extremely grateful if anyone could help me with this ... its mainly part iv) that I'm stuck on but the other parts build up to it! Thanks very much! 1. Homework Statement I have a wheel shaped space station of radius 100m rotating about its symmetry axis (defined to be the z axis) at...
  12. C

    B How can we tell that "fictitious forces" are not real?

    Earlier today I was reading through this entire thread: https://www.physicsforums.com/threads/implications-of-the-statement-acceleration-is-not-relative.670653/ And I remained confused about one thing in particular. The original poster made a statement (bolded below) on page 1 that seemed...
  13. S

    Angular momentum conservation and constant velocity as expla

    I'm confused about situations involving rotating frames in which the angular momentum is conserved and the initial velocity does not change. I'll make an example. Take a rotating carousel (constant angular velocity) with no friction on it and a ball. At the initial time instant the ball has the...
  14. 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...
  15. Quadrat

    Investigating Fictitious Forces in Car Acceleration

    Hi, I was sitting and thinking of the case where a smoke is rising from say, some incense inside of a car that is accelerating. I thought that it must act the same way as a helium balloon would have. When you turn left, the smoke tends to go left, when you accelerate in a straight line the...
  16. SpiderET

    Easier description of fictitious forces?

    It seems to me the current description of fictitious forces is too complicated. It is described as effect of accelerate non inertial frame and there are four types of fictitious forces: rectilinear acceleration force, centrifugal force, Coriolis force and Euler force. Why can't we say that...
  17. L

    Explaining Fictitious Forces in Accelerating Carts

    Let's say there is a cart with a pendulum inside it. The cart then starts accelerating, while an observer on the ground remain still. I was told that the observer, standing still, would not observe any fictitious forces on the pendulum, so how does he explain the pendulum swinging backwards?
  18. P

    Mechanics (Non-inertial systems and Fictitious Forces)

    Homework Statement A sled slides from a slope with inclination α. A man standing on the sled ‘weighs’ an object with mass m using a spring balance. What weight does the balance indicate? I seem to be making it too complex, could anyone help me out with it? Homework EquationsThe Attempt at a...
  19. P

    The Higgs field (mechanism) is the cause of fictitious forces?

    Newton second law of motion states that acceleration is produced when a force acts on a mass. The Higgs field (mechanism) is the cause of fictitious forces?
  20. electricspit

    Exploring Fictitious Forces in Classical Mechanics

    Hey! I was wondering about the concept of fictitious forces. I'm studying classical mechanics right now and we've made our way to non-inertial reference frames. One major problem I have is trying to understand the Coriolis force for an object falling. I understand that if an object is...
  21. stripes

    Fictitious Forces in a Rotating Co-ordinate System

    Homework Statement Here is the question, copied verbatim from the assignment: You are sitting on a chair in the rotating co-ordinate system, going round and round. You are sitting at the centre of a turntable in fact. Directly above the turntable, a horizontal distance R from the centre...
  22. B

    Fictitious forces in rotating frames of reference

    I got stuck going over the derivation of fictitious forces in rotating frames. see specifically http://en.wikipedia.org/wiki/Rotating_reference_frame#Time_derivatives_in_the_two_frames this page to see the proof I'm talking about (sorry i'd love to be able to explain it by myself but...
  23. P

    Fictitious forces question.

    Hi, Homework Statement I have a question concerning fictitious forces (although its first part is irrelevant to the latter): A smooth string is extended between two points A and B in a vertically positioned circle, so that the angle between the string and the vertical axis of the circle is...
  24. B

    Conceptual Question for Fictitious Forces

    Homework Statement Fictitious forces are created by people when motion is observed from non inertial F.o.r. what is the real cause of these fictitious forces? Homework Equations The Attempt at a Solution Since Fictitious force are viewed from non inertial F.o.r, the answer is...
  25. J

    Ball thrown across a carousel - fictitious forces in polar coordinates

    Homework Statement a carousel is spinning with a constant angular velocity ω. two people, A and B are standing across each other (with the center between them) at distance 2d (d is the radius of the carousel). A throws a ball to B, so B catches it after T seconds. describe the equations...
  26. L

    Pseudoforces or fictitious forces

    Homework Statement Why centrifugal force, Coriolis force are termed as psuedoforces? Are they not real forces? Please help, revered members. Homework Equations The Attempt at a Solution
  27. harrylin

    Are fictitious forces necessary to solve certain problems?

    It can be handy to ignore the Earth's rotation and simply work with the effective g', instead of accounting for g'=g+a; and similarly it may be handy to use Coriolis forces and so on for weather predictions. Nevertheless I assume that calculations with fictitious forces can always be reconverted...
  28. S

    Trouble interpreting fictitious forces for block on wedge problem

    Homework Statement This is a standard block on wedge problem - we have an incline of angle \alpha, a block of mass m on wedge of mass M. The block is released from the inclined surface. The wedge is not fixed and can accelerate. The question is typical - find the horizontal accelerations...
  29. P

    Gravity and fictitious forces

    Good evening, Suppose that there are two bodies, A and B, of masses mA and mB, in vacuum. In an arbitrary inertial reference frame, the gravitational acceleration produced by B in A is \vec{a}_A and the one produced by A in B is \vec{a}_B. Now, I want to calculate the gravitational acceleration...
  30. M

    Calculate Normal Force in Mass M & m Slope System with no Friction

    We have a slope, with mass M, at x degrees. Mass m is on the slope. The slope moves right at constant acceleration a_0. There is no friction between M and m, and no friction between M and ground. Determine the Normal Force between M and m...
  31. A

    Classical Mechanics: Fictitious Forces: Centrifugal, Coriolis, Transverse, etc.

    Homework Statement Figure is attached. In an amusement park ride called the hammer a large beam rotates in a ver- tical plane about a central pivot (see figure). Cages are attached to the end of the beam; these rotate independently. The riders are strapped to the walls of the cages. The...
  32. F

    Can we model fictitious forces using vectors?

    Homework Statement Let's say that you are on a Ferris Wheel or you are spinning a Yo-yo horizontally in a circle. There is a fictitous force known as centrifuge force that is pushing the car or yo-yo outwards. However, the centripetal force that is keeping it in tact, is a vector pointing...
  33. Y

    Solving Fictitious Forces w/ Massless Pulley

    Homework Statement All surfaces are frictionless, pulley is massless. What force, F is needed so that m3 does not rise or fall? Picture attached Homework Equations F=ma The Attempt at a Solution Found acceleration of system by dividing F by all three masses. Found...
  34. B

    Fictitious forces, and motion

    Homework Statement The first question asks: Which (fictitious) force will cause the sledge to accelerate along the rails? Give the modulus and direction of the sledge at distance r<R from the centre. The next question asks: Obtain an expression for the displacement r(t) for r<R...
  35. E

    Friction and fictitious forces

    i have a question regarding friction and fictitious forces. if two crates are lying on a flat surface, while the smaller one is on top of the bigger one, and a force of 10N is acted upon the bigger one will the smaller one be pushed backwards because of fictitous forces? and because...
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