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3.2 Lagrange-Euler Dynamics 109

Figure 3.2.1: Centripetal force.

Imagine a sphere (i.e., the earth) rotating about its center with an angular
velocity of ω 0 . See Figure 3.2.2. The Coriolis force on a body of mass m
moving with velocity v on the surface of the sphere is given by

F cor =-2mω 0 ×v (3.2.3)

Using the right-handed screw rule (i.e., if the fingers rotate ω 0 into v, the
thumb points in the direction of ω 0×v, we see that, in the figure, the Coriolis
force acts to deflect m to the right.
In a low-pressure weather system, the air mass moves toward the center
of the low. The Coriolis force is responsible for deflecting the air mass to the
right and so causing a counterclockwise circulation known as cyclonic flow.
The result is the swirling motion in a hurricane. A brief examination of
Figure 3.2.2 reveals that in the southern hemisphere F cor deflects a moving
mass to the left, so that a low-pressure system would have a clockwise wind
motion.
Since and we may write

(3.2.4)

It is important to note that the centripetal force involves the square of a
single angular velocity, while the Coriolis force involves the product of two
distinct angular velocities.
The kinetic energy of a mass moving with a linear velocity of v is

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