Pseudoforces

Pseudoforces are forces which aren't really there. Why, then, you might well ask, do we deal with them? The answer is because it is psychologically and occassionally computationally useful to do so.

Pseudoforces (think of them as Sears forces, not real forces - F. Zappa) are useful to describe the apparent total force acting on an object in a non-inertial reference frame. A non-inertial reference frame is one that is accelerating. Since the object may be accelerating inside the frame because of real forces acting on it, and the frame itself is accelerating, we have to add the two of these things to get the acceleration relative to the frame. The (mass times the) acceleration of the frame thus looks like an additional force that is acting on the object in the frame to produce its total acceleration in frame coordinates.

Various pseudoforces we will encounter in problems in the next few weeks are:

1. The force added or subtracted to a real force (i.e. - mg, or a normal force) in a frame accelerating uniformly (see picture above).
2. The ``centrifugal'' force that apparently acts on an object in a rotating frame. Note that this is just minus the real centripetal force that pushes the object toward the center. The centrifugal force is the normal force that a scale might read as it provides the centripetal push.
3. Rotating frames actually account for lots of pseudoforces. There are also pseudoforces acting on objects falling towards or away from a rotating sphere. These forces describe the apparent deflection of a particle as its straight-line trajectory falls ahead of or behind the rotating frame (in which the "rest" velocity is a function of $\omega$ and $r$).
4. Finally, objects moving north or south along the surface of a rotating sphere also experience a similar deflection, for similar reasons. As a particle moves towards the equator, it is suddenly travelling too slowly for its new radius (and constant $\omega$) and is apparently ``deflected'' west. As it travels away from the equator it is suddenly traveling too fast for its new radius and is deflected east. These effects combine to produce clockwise rotation of large air masses in the northern hemisphere and anticlockwise rotations in the southern hemisphere.

   Note Well: Hurricanes rotate counterclockwise in the northern hemisphere because the counterclockwise winds meet to circulate the other way around a defect at the center. This defect is called the ``eye''. Winds flowing into a center have to go somewhere. At the defect they must go up or down. In a hurricane the ocean warms air that rushes toward the center and rises. This warm wet air dumps (warm) moisture and cools. The cool air circulates far out and gets pulled back along the ocean surface, warming as it comes in. A hurricane is a heat engine!

5. The two forces just mentioned (pseudoforces in a rotating frame) are commonly called coriolis forces and are a major driving factor in the time evolution of weather patterns. They also complicate naval artillery trajectories, missile launches (as the coriolis forces combine with drag forces to produce very real and somewhat unpredictable deflections), and will one day make pouring a drink in a space station an interesting process (hold the cup just a bit antispinward, as things will not - apparently - fall in a straight line!).