In
classical mechanics
Classical mechanics is a Theoretical physics, physical theory describing the motion of objects such as projectiles, parts of Machine (mechanical), machinery, spacecraft, planets, stars, and galaxies. The development of classical mechanics inv ...
, the Euler force is the
fictitious tangential force
that appears when a non-uniformly
rotating reference frame is used for analysis of motion and there is variation in the
angular velocity
In physics, angular velocity (symbol or \vec, the lowercase Greek letter omega), also known as the angular frequency vector,(UP1) is a pseudovector representation of how the angular position or orientation of an object changes with time, i ...
of the
reference frame's axes. The Euler acceleration (named for
Leonhard Euler
Leonhard Euler ( ; ; ; 15 April 170718 September 1783) was a Swiss polymath who was active as a mathematician, physicist, astronomer, logician, geographer, and engineer. He founded the studies of graph theory and topology and made influential ...
), 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 (symbol or \vec, the lowercase Greek letter omega), also known as the angular frequency vector,(UP1) is a pseudovector representation of how the angular position or orientation of an object changes with time, i ...
of the
reference frame.
Intuitive example
The Euler force will be felt by a person riding a
merry-go-round. 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
*
Coriolis effect
*
Centrifugal force
*
Rotating reference frame
*
Angular acceleration
Notes and references
Fictitious forces
Rotation
{{classicalmechanics-stub