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 classical ...

, 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 onl ...

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 objec ...

of the

reference frame In physics and astronomy, a frame of reference (or reference frame) is an abstract coordinate system whose origin (mathematics), origin, orientation (geometry), orientation, and scale (geometry), scale are specified by a set of reference point ...

'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 in ma ...

), also known as azimuthal acceleration or transverse acceleration is that part of the absolute acceleration that is caused by the variation in the

of the

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 (List of sovereign states, international), roundabout (British English), or hurdy-gurdy (an old term in Australian English, in South Australia, SA) is a type of amusement ...

. 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: :

\mathbf_\mathrm = - \frac \times \mathbf,

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 :

\mathbf_\mathrm = m \mathbf_\mathrm = - m \frac \times \mathbf.

Notes and references

Fictitious forces Rotation {{classicalmechanics-stub

Intuitive example

Mathematical description

See also

Notes and references