## Quick Reference

A force that may be assumed to exist by an observer whose frame of reference is accelerating relative to an inertial frame of reference. Suppose, for example, that a frame of reference with origin *O* is rotating relative to an inertial frame of reference with the same origin. A particle *P* subject to a certain total force satisfies Newton's second law of motion, relative to the inertial frame of reference. To the observer in the rotating frame, the particle appears to satisfy an equation of motion that is Newton's second law of motion with additional terms. The observer may suppose that these terms are explained by certain fictitious forces. When these forces are assumed to exist, Newton's laws appear to hold in the non-inertial frame of reference.

Consider the special case in which the rotating frame of reference has a constant angular velocity and the particle is moving in a plane perpendicular to the angular velocity of the rotating frame of reference. One fictitious force is in the direction along *OP* and is called the centrifugal force. This is the force outwards that is believed to exist by a rider on a roundabout. The second fictitious force is perpendicular to the path of *P* as seen by the observer in the rotating frame of reference and is called the Coriolis force.

To an observer standing on the Earth, which is rotating about its axis, an object such as an intercontinental missile appears to deviate from its path due to the Coriolis force. The deviation is to the right in the northern hemisphere and to the left in the southern hemisphere. This force, first described by the French mathematician and engineer, Gustave-Gaspard de Coriolis (1792–1843), also has important applications to the movement of air masses in meteorology.

Similar fictitious forces may arise whenever the observer's frame of reference is accelerating relative to an inertial frame of reference, as when a passenger in an accelerating lift witnesses a ceiling tile fall from the roof of the cabin.

*Subjects:*
Mathematics.