In
classical mechanics
Classical mechanics is a physical theory describing the motion of macroscopic objects, from projectiles to parts of machinery, and astronomical objects, such as spacecraft, planets, stars, and galaxies. For objects governed by classi ...
, the Euler force is the
fictitious tangential force
that appears when a non-uniformly
rotating reference frame
A rotating frame of reference is a special case of a non-inertial reference frame that is rotating relative to an inertial reference frame. An everyday example of a rotating reference frame is the surface of the Earth. (This article considers only ...
is used for analysis of motion and there is variation in the
angular velocity
In physics, angular velocity or rotational velocity ( or ), also known as angular frequency vector,(UP1) is a pseudovector representation of how fast the angular position or orientation of an object changes with time (i.e. how quickly an object ...
of the
reference frame
In physics and astronomy, a frame of reference (or reference frame) is an abstract coordinate system whose origin, orientation, and scale are specified by a set of reference points― geometric points whose position is identified both math ...
's axes. The Euler acceleration (named for
Leonhard Euler
Leonhard Euler ( , ; 15 April 170718 September 1783) was a Swiss mathematician, physicist, astronomer, geographer, logician and engineer who founded the studies of graph theory and topology and made pioneering and influential discoveries ...
), also known as azimuthal acceleration
or transverse acceleration
is that part of the absolute acceleration that is caused by the variation in the
angular velocity
In physics, angular velocity or rotational velocity ( or ), also known as angular frequency vector,(UP1) is a pseudovector representation of how fast the angular position or orientation of an object changes with time (i.e. how quickly an object ...
of the
reference frame
In physics and astronomy, a frame of reference (or reference frame) is an abstract coordinate system whose origin, orientation, and scale are specified by a set of reference points― geometric points whose position is identified both math ...
.
Intuitive example
The Euler force will be felt by a person riding a
merry-go-round
A carousel or carrousel (mainly North American English), merry-go-round ( international), roundabout (British English), or hurdy-gurdy (an old term in Australian English, in SA) is a type of amusement ride consisting of a rotating circular ...
. As the ride starts, the Euler force will be the apparent force pushing the person to the back of the horse; and as the ride comes to a stop, it will be the apparent force pushing the person towards the front of the horse. A person on a horse close to the perimeter of the merry-go-round will perceive a greater apparent force than a person on a horse closer to the axis of rotation.
Mathematical description
The direction and magnitude of the Euler acceleration is given, in the rotating reference frame, by:
:
where ω is the angular velocity of rotation of the reference frame and r is the vector position of the point in the reference frame. The Euler force on an object of mass ''m'' in the rotating reference frame is then
:
See also
*
Fictitious force
A fictitious force is a force that appears to act on a mass whose motion is described using a non-inertial frame of reference, such as a linearly accelerating or rotating reference frame.
It is related to Newton's second law of motion, which trea ...
*
Coriolis effect
In physics, the Coriolis force is an inertial or fictitious force that acts on objects in motion within a frame of reference that rotates with respect to an inertial frame. In a reference frame with clockwise rotation, the force acts to the ...
*
Centrifugal force
In Newtonian mechanics, the centrifugal force is an inertial force (also called a "fictitious" or "pseudo" force) that appears to act on all objects when viewed in a rotating frame of reference. It is directed away from an axis which is paralle ...
*
Rotating reference frame
A rotating frame of reference is a special case of a non-inertial reference frame that is rotating relative to an inertial reference frame. An everyday example of a rotating reference frame is the surface of the Earth. (This article considers only ...
*
Angular acceleration
In physics, angular acceleration refers to the time rate of change of angular velocity. As there are two types of angular velocity, namely spin angular velocity and orbital angular velocity, there are naturally also two types of angular accelera ...
Notes and references
Fictitious forces
Rotation
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