User:John R. Brews/Coriolis force

The Coriolis force is a force experienced by a object traversing a path in a rotating framework that is proportional to its speed and also to the sine of the angle between its direction of movement and the axis of rotation. It is one of three such inertial forces that appear in an accelerating frame of reference due to the acceleration of the frame, the other two being the centrifugal force and the Euler force. The mathematical expression for the Coriolis force appeared in an 1835 paper by a French scientist Gaspard-Gustave Coriolis in connection with the theory of water wheels, and also in the tidal equations of Pierre-Simon Laplace in 1778.

Although sometimes referred to as an apparent force, it can have very real effects.

Reference frames

Newton's laws of motion are expressed for observations made in an inertial frame of reference, that is, in any frame of reference that is in straight-line motion at constant speed relative to the "fixed stars", an historical reference taken today to refer to the entire universe. However, everyday experience does not take place in such a reference frame. For example, we live upon planet Earth, which rotates about its axis (an accelerated motion), orbits the Sun (another accelerated motion), and moves with the Milky Way (still another accelerated motion).

The question then arises as to how to connect experiences in accelerating frames with Newton's laws that are not formulated for such situations. The answer lies in the introduction of inertial forces, which are forces observed in the accelerating reference frame, due to its motion, but are not forces recognized in an inertial frame. These inertial forces are included in Newton's laws of motion, and with their inclusion Newton's laws work just as they would in an inertial frame. Coriolis force is one of these inertial forces, the other two being the centrifugal force and the Euler force.

These motions are slight, but the Coriolis force does affect aiming artillery pieces and plotting transoceanic air flights. The way Coriolis forces work is illustrated below by a few examples.

Foucault pendulum

The Foucault pendulum, or Foucault's pendulum, demonstrated in Paris in 1851, is named after the French physicist Léon Foucault. It is a device that demonstrates the rotation of the Earth. According to an inertial observer, the pendulum swings in a plane fixed relative to the "fixed stars", while as observed on Earth this plane appears to rotate. For most pendulums, the effect is masked by other complications, so some care must be taken in constructing a successful pendulum.

The easiest way to understand the operation is to imagine the pendulum at the North pole. As the pendulum swings, the Earth rotates and it appears to the Earth-bound observer that every 24 hours the pendulum returns to its initial plane of oscillation. The Earth-bound observer explains the behavior using Newton's laws by including the Coriolis force:

$\mathbf {F_{\mathrm {Cor} }} =2m\mathbf {v\times \Omega } \ ,$

where m is the mass of the pendulum, v its velocity and Ω a vector along the axis of rotation with magnitude ω, the angular rate of rotation in radians/s. Writing the force equation for the bob, in the frame of the bob:

$m\mathbf {a} =\mathbf {F_{T}} -m\mathbf {g} -2m\mathbf {\Omega \times v} +m\omega ^{2}\mathbf {r} \ ,$

where F_T is the tension in the string, mg is the force of gravity and the last term is the centrifugal force on the bob. http://books.google.com/books?id=-3H5V0LGBOgC&pg=PA122&dq=Foucault+pendulum&hl=en&ei=CV1gTenZOpGisQO9ruzNCA&sa=X&oi=book_result&ct=result&resnum=9&ved=0CGQQ6AEwCA#v=onepage&q=Foucault%20pendulum&f=false http://books.google.com/books?id=NAo7yv7Jmq0C&pg=PA22&dq=Foucault+pendulum&hl=en&ei=VYVgTcujHoOusAO0vOXNCA&sa=X&oi=book_result&ct=result&resnum=1&ved=0CCoQ6AEwADgK#v=onepage&q=Foucault%20pendulum&f=false