The magnitude of the Coriolis force is proportional to the rotation rate, and the magnitude of the centrifugal force is proportional to the square of the rotation rate. When applied to objects with masses, the respective forces are proportional to their masses. When Newton's laws are transformed to a rotating frame of reference, the Coriolis and centrifugal accelerations appear. Newton's laws of motion describe the motion of an object in an inertial (non-accelerating) frame of reference. Early in the 20th century, the term Coriolis force began to be used in connection with meteorology. Though recognized previously by others, the mathematical expression for the Coriolis force appeared in an 1835 paper by French scientist Gaspard-Gustave de Coriolis, in connection with the theory of water wheels. Deflection of an object due to the Coriolis force is called the Coriolis effect. In one with anticlockwise (or counterclockwise) rotation, the force acts to the right. In a reference frame with clockwise rotation, the force acts to the left of the motion of the object. 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. However, the observer (red dot) who is standing in the rotating/non-inertial frame of reference (lower part of the picture) sees the object as following a curved path due to the Coriolis and centrifugal forces present in this frame. In the inertial frame of reference (upper part of the picture), the black ball moves in a straight line.
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