Magnitude and Direction of Forces

Coriolis Force

All measurements are relative to some standard. Motion is measured relative to a reference frame. It is common to assume that this reference frame is at rest, or moving at constant velocity with respect to the fixed stars. Newton's laws of motion are defined with respect to a fixed reference frame. Everything in the room around you is in motion, anchored to the ground by gravity and continually spinning with the earth. Walls appear to be at rest because you are moving with them, the relative motion is zero.

There is no problem in assuming a fixed reference frame when measuring the movement of a ball during a game of catch, or how water drains from a sink. However, using a fixed reference frame sires a riddle when measuring motions on earth over large distances; objects do not appear to travel in a straight line! Imagine planning the launch of a space-craft from the North Pole so that it lands in Europe. In planning our launch, we follow Newton's First Law and aim the space-craft at Europe; however, it lands in the Midwest United States. As the space-craft is in the air, the earth rotates underneath, causing a miss of our intended target. The space-craft is traveling in a straight line, but because the earth is moving, the path appears to be curved with reference to the ground. A change in the direction of travel of an object requires a force, and so it appears that a force is accelerating the space-craft to the right. As seen from space looking down over the North Pole, the world rotates counterclockwise. Looking down on the South Pole the world rotates clockwise. If the space-craft were launched from the South Pole, it would appear to be deflected to the left, as the earth spins clockwise when looking down on the Southern Hemisphere from space.

We have two choices for a successful landing. One is to change our reference for measuring motion to an inertial reference frame, for example with reference to a fixed point in space. Using an inertial reference frame we deal only with real forces and account for the moving earth. The second choice is to keep with our original noninertial frame of reference and consider real forces and suitably defined imaginary or apparent forces. In meteorology, the second option is chosen as a matter of convenience.

Newton's laws of motion are defined with respect to a fixed reference frame. However, Earth is moving and so we must include an apparent force that accounts for our moving reference frame. This apparent force is called the Coriolis force. Having selected a noninertial reference frame, we must now describe what determines the magnitude and direction of the Coriolis force. The magnitude of the Coriolis force is proportional to the speed of the wind. If the wind speed is zero, there is no relative motion and the Coriolis force is zero. An object's inertia increases with speed, so a larger force is required to change its direction of travel. The Coriolis force increases with increasing wind speed. The Coriolis force acts perpendicular to the direction of motion (to the right of the wind in the Northern Hemisphere) and therefore cannot change the wind speed. The Coriolis force cannot generate a wind, it can only change its direction. The magnitude of the Coriolis force depends on latitude. At the equator the Coriolis force is zero and it increases towards the poles.

Mathematically the magnitude of the Coriolis force is written

The constant, 0.000146, is defined by the rotation rate of earth and has units of per second. V is the wind speed in meters per second.

We have to consider the Coriolis effect only when dealing with winds that travel over long distances. It takes only a few seconds for a thrown ball to reach its destination. During this time the earth has hardly moved and the deflection of the ball's path is insignificant. Since we do not have to adjust for the Coriolis force when playing football, soccer, tennis, or Ping-Pong, or monkey-in-the-middle, there is no reason to assume that the Coriolis force has anything to do with the spinning motion of a flushed toilet. However, play catch on a rapidly revolving merry-go-round, with one person in the center and the other on the outer edge. When thrown, the ball will appear to curve away from its intended target.