Coriolis effect

This animation is relatively abstract; it presents the underlying characteristic that the various cases where the Coriolis effect is at play have in common. The various cases are discussed in separate articles. If you are interested in the case of wind and atmosphere then go to the rotation of Earth effect that is taken into account in Meteorology.

This animation forms part of a pair of rotation effect physlets. The other rotation effect physlet is the centrifugal effect physlet.

Also available: a 3D simulation (Java applet), called inertial oscillation, which presents the rotation-of-Earth effect that is essentially the same as the rotation effect in this animation.

The controls

When you change something in the checkboxes then the change will become effective when you press the PLAY button again. You can first reset the simulation and then press PLAY, or you can press PLAY while the animation is still running.

Evolution of the display

This animation represents the case of frictionless motion of an object that experiences a centripetal force. More specifically, the strength of the centripetal force is proportional to the distance to the central axis of rotation. A proportional centripetal force is very symmetrical and the motion under the influence of that force has distinctive properties.

You can set the left-right distance to zero, and the top-bottom distance to some non-zero value and then the motion will be a simple harmonic oscillation. Conversely, you can let the animation display a left-right harmonic oscillation. Any trajectory enforced by the proportional centripetal force can be thought of as a combination of two perpendicular harmonic oscillations.

Motion under the influence of a proportional centripetal force has the following significant property: all trajectories have the same period of revolution. Further away from the center a stronger centripetal force is required, and a proportional centripetal force provides just that. So no matter how close to the center or how far: for every object the time to complete a circumnavigation is the same. It also does not matter whether the trajectory is circular or ellipse-shaped, the period is always the same. The obvious choice of rotating coordinate system is the one that matches that invariant period; if you set 'left-right' and 'top-bottom' to the same distance (Press PLAY to make that change effective) then the object is stationary with respect to the co-rotating coordinate system.

Decomposition of the motion

Check the boxes for 'trajectories' and 'circle and epi-circle'. (Pressing 'PLAY' once more to make that change effective.) Then you see another elegant way of decomposing the ellipse-shaped trajectory in two components; a circle and an epi-circle. The center of the epi-circle moves in uniform circular motion around the central axis, the object moves in uniform circular motion along the epi-circle. When the overall rotation is counterclockwise (as in this example) then the motion along the main circle proceeds counterclockwise and the motion along the epi-circle proceeds clockwise.

Eccentricity

The motion along the epi-circle represents the eccentricity of the trajectory.

Transformation to a co-rotating coordinate system removes the motion along the main circle; the eccentricity remains. Also, note that as seen from a co-rotating point of view the motion along the epi-circle cycles twice for every cycle of the system as a whole.

The most efficient way to describe the acceleration with respect to the co-rotating system is to follow the decomposition in circle and epi-circle. Check the box for 'Coriolis & centrifugal'. The centrifugal vector is proportional to the distance to the central axis of rotation, the Coriolis vector represents the acceleration that corresponds with the uniform circular motion along the epi-circle.

The main circle and the epi-circle are indeed perfect circles and the motion along them is uniform. The mathematical proof for that is remarkably simple, you can find it in the article about rotational-vibrational coupling

Similar for all directions of motion

A defining characteristic of the Coriolis effect is that the acceleration with respect to the rotating system is the same for any direction of velocity relative to the rotating system.

As mentioned at the start: the strength of the centripetal force is proportional to the distance to the central axis of rotation. So whenever the object is circumnavigating slower than the rotating system the object experiences a surplus of centripetal force, and then this surplus pulls the object closer to the central axis of rotation.

Centripetal force and inertia

The rotation effect represented here arises from the centripetal force and inertia conjointly.

When the object is pulled closer to the central axis of rotation the centripetal force is doing work. When the object has reached its point of closest approach its subsequent motion is dominated by its inertia; the object's velocity has become so large that its inertia carries it away from the central axis again. During motion away from the central axis the energy conversion is accounted for in the form of the centripetal force doing negative work.

Addition of another force

In this simulation there is only one force affecting the trajectory of the object; the centripetal force. Imagine what would happen if there are other forces affecting the object. For example the object can be deflected with a gust of air. With another force added the dynamics will be determined by the sum of the two influences.

For example, a temporary gust of air directed against the object will shift it from one ellipse-shaped trajectory to another ellipse-shaped trajectory, and during that shift the Coriolis effect will continue to be at play.

Adjustment to rotation state

An assembly of interconnected parts that is rotating will always self-adjust to some equilibrium state: for example, if you attach a weight to a spring, and you swing the weight around then the spring will extend until the point is reached where the contractive force of the spring exerts the required centripetal force. In general, after a change of angular velocity a rotating system will go through a readjustment phase that ends with reaching once more a state of dynamic equilibrium. (If there is insufficient centripetal force the parts will simply fly apart.) At every distance to the central axis of rotation the amount of centripetal force will be the amount that is necessary for sustaining co-rotating motion.

Ballistics is different

There is in physics one example where there is no centripetal force at play: ballistics. In the case of ballistics, for cases where friction can be ignored, there is in fact no physical interaction between the moving object and the rotating system and consequently ballistics is very different from other areas of mechanics. The case of ballistics is depicted in the interactive animation centrifugal effect

Rotation-of-Earth effect

As mentioned at the start of this article, you can also try the following 3D simulation, called inertial oscillation, which presents the rotation-of-Earth effect that is the terrestrial counterpart of the rotation effect in this simulation.

Text, images and animations are licensed under a Creative Commons Attribution-ShareAlike 2.5 License.

The physlet simulation environment has been created by Davidson College.

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Last time this page was modified: January 23 2010