page_title: Coriolis force
section_title: Intuitive example
hierarchical_section_title: Coriolis force / Applied to the Earth / Eötvös effect / Intuitive example
caption_attribution_description: English: Graph of the force experienced by a 10 kilograms object as a function of it's speed moving along Earth's equator (as measured within the rotating frame). (Positive force in the graph is directed upward. Positive speed is directed eastward and negative speed is directed westward).
context_page_description: In physics, the Coriolis force is an inertial or fictitious force that acts on objects that are in motion within a frame of reference that rotates with respect to an inertial frame. In a reference frame with clockwise rotation, the force acts to the left of the motion of the object. In one with anticlockwise rotation, the force acts to the right. Deflection of an object due to the Coriolis force is called the Coriolis effect. Though recognized previously by others, the mathematical expression for the Coriolis force appeared in an 1835 paper by French scientist Gaspard-Gustave de Coriolis, in connection with the theory of water wheels. Early in the 20th century, the term Coriolis force began to be used in connection with meteorology.
  Newton's laws of motion describe the motion of an object in an inertial frame of reference. When Newton's laws are transformed to a rotating frame of reference, the Coriolis and centrifugal accelerations appear. When applied to massive objects, the respective forces are proportional to the masses of them. The Coriolis force is proportional to the rotation rate and the centrifugal force is proportional to the square of the rotation rate.
context_section_description: Imagine a train that travels through a frictionless railway line along the equator. Assume that, when in motion, it moves at the necessary speed to complete a trip around the world in one day (465 m/s). The Coriolis effect can be considered in three cases: when the train travels west, when it is at rest, and when it travels east. In each case, the Coriolis effect can be calculated from the rotating frame of reference on Earth first, and then checked against a fixed inertial frame. The image below illustrates the three cases as viewed by an observer at rest in a (near) inertial frame from a fixed point above the North Pole along the Earth's axis of rotation; the train is denoted by a few red pixels, fixed at the left side in the leftmost picture, moving in the others 
  1. The train travels toward the west: In that case, it moves against the direction of rotation. Therefore, on the Earth's rotating frame the Coriolis term is pointed inwards towards the axis of rotation (down). This additional force downwards should cause the train to be heavier while moving in that direction.
  If one looks at this train from the fixed non-rotating frame on top of the center of the Earth, at that speed it remains stationary as the Earth spins beneath it. Hence, the only force acting on it is gravity and the reaction from the track. This force is greater (by 0.34%) than the force that the passengers and the train experience when at rest (rotating along with Earth). This difference is what the Coriolis effect accounts for in the rotating frame of reference.
  2. The train comes to a stop: From the point of view on the Earth's rotating frame, the velocity of the train is zero, thus the Coriolis force is also zero and the train and its passengers recuperate their usual weight.
  From the fixed inertial frame of reference above Earth, the train now rotates along with the rest of the Earth. 0.34% of the force of gravity provides the centripetal force needed to achieve the circular motion on that frame of reference. The remaining force, as measured by a scale, makes the train and passengers "lighter" than in the previous case.
  3. The train travels east. In this case, because it moves in the direction of Earth's rotating frame, the Coriolis term is directed outward from the axis of rotation (up). This upward force makes the train seem lighter still than when at rest.
  From the fixed inertial frame of reference above Earth, the train travelling east now rotates at twice the rate as when it was at rest—so the amount of centripetal force needed to cause that circular path increases leaving less force from gravity to act on the track. This is what the Coriolis term accounts for on the previous paragraph.
  As a final check one can imagine a frame of reference rotating along with the train. Such frame would be rotating at twice the angular velocity as Earth's rotating frame. The resulting centrifugal force component for that imaginary frame would be greater. Since the train and its passengers are at rest, that would be the only component in that frame explaining again why the train and the passengers are lighter than in the previous two cases.
  This also explains why high speed projectiles that travel west are deflected down, and those that travel east are deflected up. This vertical component of the Coriolis effect is called the Eötvös effect.
  The above example can be used to explain why the Eötvös effect starts diminishing when an object is travelling westward as its tangential speed increases above Earth's rotation (465 m/s). If the westward train in the above example increases speed, part of the force of gravity that pushes against the track accounts for the centripetal force needed to keep it in circular motion on the inertial frame. Once the train doubles its westward speed at 930 m/s that centripetal force becomes equal to the force the train experiences when it stops. From the inertial frame, in both cases it rotates at the same speed but in the opposite directions. Thus, the force is the same cancelling completely the Eötvös effect. Any object that moves
caption: Graph of the force experienced by a 10-kilogram object as a function of its speed moving along Earth's equator (as measured within the rotating frame). (Positive force in the graph is directed upward. Positive speed is directed eastward and negative speed is directed westward).
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