Friday, Mar 31, 2006 at 08:03
And more!!!
This entry contributed by Leonardo Motta
The Coriolis force is a fictitious force exerted on a body when it moves in a rotating reference frame. It is called a fictitious force because it is a by-product of measuring coordinates with respect to a rotating coordinate system as opposed to an actual "push or pull."
As an example, suppose an observer is sitting on a carousel that appears to him to be stationary but, from the point of view of an outside observer standing on the ground, the carousel is rotating with angular velocity . Now suppose that the carousel rider moves a ball with mass m radially away from the center of the carousel. From the point of view of the observer outside, the ball moves in a curved path which is tangent to the center of rotation. Since the ball's path is curved in inertial space, there must be a force to accelerate it, and this force is called the Coriolis force. The Coriolis force can be observed directly in satellite tracking of hurricanes, whose paths can clearly be seen to curve to the right in the northern hemisphere and to the left in the southern hemisphere as their distances from the Earth's rotation changes.
To compute the Coriolis force, note that the ball moved by the carousel rider has angular velocity , so its angular momentum is
(1)
When the mass is close to the center, it has relatively little angular momentum, but as it moves farther out (increasing r), it has greater angular momentum. Therefore, a torque must be exerted in order to move it along the radius, and that torque is the rate of change of L with time as m moves along the radius. If m moves entirely radially, that stays constant and the torque is given by
(2)
where is the Coriolis force.
The Coriolis force is therefore the sidewise force that has to be exerted by the carousel rider to cause the ball to move outward at a radial speed which, upon solving (2), is
(3)
In vector notation, the Coriolis force is given by
(4)
(5)
(6)
where is the Coriolis acceleration. It can therefore be seen that The Coriolis force independent of radius, and is present even at the origin of the rotating coordinate system.
Coriolis Acceleration, Coriolis Frequency, Coriolis Parameter, Rossby Number
Coriolis, G.-G. "Sur les équations du mouvement relatif des systèmes de corps." J. de l'Ecole royale polytechnique 15, 144-154, 1835.
Feynman, R. P.; Leighton, R. B.; and Sands, M. The Feynman Lectures on Physics, Vol. 1. Redwood City, CA: Addison-Wesley, pp. 19-8-19-9, 1989.
French, A. P. Newtonian Mechanics. New York: W. W. Norton, pp. 528-529, 1971.
© 1996-2006 Eric W. Weisstein
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