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Euler force
 
 
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In classical mechanics
Classical mechanics

Classical mechanics is used for describing the motion of macroscopic objects, from projectiles to parts of machinery, as well as astronomical objects, such as spacecraft, planets, stars, and galaxies....
, the Euler acceleration (named for Leonhard Euler
Leonhard Euler

Leonhard Paul Euler was a pioneering Swiss mathematician and physicist who spent most of his life in Russia and Germany.Euler made important discoveries in fields as diverse as calculus and graph theory....
), also known as azimuthal acceleration or transverse acceleration is an acceleration
Acceleration

File:Acceleration.JPGFile:Acceleration components.JPGIn physics, and more specifically kinematics, acceleration is the change in velocity over time....
 that appears when a non-uniformly rotating reference frame
Rotating reference frame

A rotating frame of reference is a special case of a non-inertial reference frame that is rotation relative to an inertial reference frame. An everyday example of a rotating reference frame is the surface of the Earth....
 is used for analysis of motion and there is variation in the angular velocity
Angular velocity

In physics, the angular velocity is a vector quantity which specifies the angular speed, and axis about which an object is rotating. The SI unit of angular velocity is radians per second, although it may be measured in other units such as degrees per second, revolutions per second, degrees per hour, etc....
 of the reference frame
Frame of reference

A frame of reference in physics, may refer to a coordinate system or Cartesian coordinate system within which to measure the position, orientation , and other properties of objects in it, or it may refer to an observational reference frame tied to the state of motion of an Observer ....
's axes. This article is restricted to a frame of reference that rotates about a fixed axis.

The Euler force is a fictitious force
Fictitious force

A fictitious force, also called a pseudo force, d'Alembert force or inertial force, is an apparent force that acts on all masses in a non-inertial reference frame, such as a rotating reference frame....
 on a body that is related to the Euler acceleration by F  = m  a , where a is the Euler acceleration and m is the mass of the body.






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In classical mechanics
Classical mechanics

Classical mechanics is used for describing the motion of macroscopic objects, from projectiles to parts of machinery, as well as astronomical objects, such as spacecraft, planets, stars, and galaxies....
, the Euler acceleration (named for Leonhard Euler
Leonhard Euler

Leonhard Paul Euler was a pioneering Swiss mathematician and physicist who spent most of his life in Russia and Germany.Euler made important discoveries in fields as diverse as calculus and graph theory....
), also known as azimuthal acceleration or transverse acceleration is an acceleration
Acceleration

File:Acceleration.JPGFile:Acceleration components.JPGIn physics, and more specifically kinematics, acceleration is the change in velocity over time....
 that appears when a non-uniformly rotating reference frame
Rotating reference frame

A rotating frame of reference is a special case of a non-inertial reference frame that is rotation relative to an inertial reference frame. An everyday example of a rotating reference frame is the surface of the Earth....
 is used for analysis of motion and there is variation in the angular velocity
Angular velocity

In physics, the angular velocity is a vector quantity which specifies the angular speed, and axis about which an object is rotating. The SI unit of angular velocity is radians per second, although it may be measured in other units such as degrees per second, revolutions per second, degrees per hour, etc....
 of the reference frame
Frame of reference

A frame of reference in physics, may refer to a coordinate system or Cartesian coordinate system within which to measure the position, orientation , and other properties of objects in it, or it may refer to an observational reference frame tied to the state of motion of an Observer ....
's axes. This article is restricted to a frame of reference that rotates about a fixed axis.

The Euler force is a fictitious force
Fictitious force

A fictitious force, also called a pseudo force, d'Alembert force or inertial force, is an apparent force that acts on all masses in a non-inertial reference frame, such as a rotating reference frame....
 on a body that is related to the Euler acceleration by F  = m  a , where a is the Euler acceleration and m is the mass of the body.

Euler acceleration

The direction and magnitude of the Euler acceleration is given by:

where:
ω is the angular velocity of rotation of the reference frame;
r is the vector position of the point where the acceleration is measured relative to the axis of the rotation.


Euler force

Using the above acceleration, the Euler force is:

where:
m is the mass
Mass

In physical science, mass refers to the degree of acceleration a body acquires when subject to a force: bodies with greater mass are accelerated less by the same force....
 of the object upon which this fictitious force
Fictitious force

A fictitious force, also called a pseudo force, d'Alembert force or inertial force, is an apparent force that acts on all masses in a non-inertial reference frame, such as a rotating reference frame....
 is exerted.


See also

  • Fictitious force
    Fictitious force

    A fictitious force, also called a pseudo force, d'Alembert force or inertial force, is an apparent force that acts on all masses in a non-inertial reference frame, such as a rotating reference frame....
  • Coriolis effect
    Coriolis effect

    In physics, the Coriolis effect is an apparent deflection of moving objects when they are viewed from a rotating reference frame.Newton's laws of motion govern the motion of an object in an inertial frame of reference....
  • Centrifugal force
    Centrifugal force

    In classical mechanics, centrifugal force is an outward force associated with rotation. Centrifugal force is one of several so-called pseudo-forces , so named because, unlike Fundamental interaction, they do not originate in interactions with other bodies situated in the environment of the particle upon which they act....
  • Rotating reference frame
    Rotating reference frame

    A rotating frame of reference is a special case of a non-inertial reference frame that is rotation relative to an inertial reference frame. An everyday example of a rotating reference frame is the surface of the Earth....