Motion, laws Coriolis force

A comparison of equations (7.103) and (7.104) shows that the Newton s second law of motion in the inertial frame O is identical in form to that in O except that the latter formulation contains several additional fictitious body forces. The term —2mil x v is the Coriolis force, and —mQ x (f2 x r) designates the centrifugal force. No name is in general use for the term — x r. The acceleration —ao compensates for the translational acceleration of the frame. 

There is also a Coriolis force that vanishes as the body s velocity in the rotating local frame approaches zero. The centrifugal and Coriohs forces are apparent or fictitious forces, in the sense that they are caused by the acceleration of the rotating frame rather than by interactions between particles. When we treat these forces as if they are real forces, we can use Newton s second law of motion to relate the net force on a body and the body s acceleration in the rotating frame (see Sec. G.6). 

It is understood that the distances and velocities associated with these two laws are determined relative to an inertial frame and that the torque and angular momentum are measured relative to the same fixed point. It is important to note that an inertial frame is a frame in which these laws hold, thus, it must be found by experiment. In his study of the motion of Mars about the sun, Newton found that the stars provided a satisfactory inertial frame. For many engineering problems, a frame fixed relative to the earth can be used as an inertial frame however, this is not the case for large scale meteorological phenomena for which the rotation of the earth produces an acceleration referred to as the Coriolis force (Dutton, 1976). 

In most textbooks the apparent forces, like the Coriolis and the centrifugal forces, are derived with the help of the framework of classical mechanics of a point particle. To examine the elementary mathematical operations involved in Newtonian mechanics, for example, we describe the motion of a material particle by the Newton s second law of motion. The Newtonian frame of reference adopted is henceforth named O. The moving relative reference frame is designated 6. The basic task is thus to transform the Newton s second law of motion as formulated in an inertial frame of reference into a relative rotating frame of reference. 

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