Coriolis Force

Deflecting inertial force acting on moving objects observed in rotating reference systems.

General idea of the topic

The Coriolis force appears in a rotating frame when a body moves relative to it. It is perpendicular to the relative velocity and to the rotation axis, equals twice the mass times the vector product of the angular velocity and the relative velocity, and does no work because it is always perpendicular to the displacement.

Unlike the centrifugal force, which also acts on bodies at rest in the rotating frame, the Coriolis force exists only if there is relative motion. It deflects the path: to the right in the northern hemisphere and to the left in the southern one, for the Earth's rotation, which explains the direction of winds and large-scale currents.

What the student is expected to understand

By the end, the student should be able to compute the Coriolis force for a body moving in a rotating frame, indicate which way it deflects and estimate whether its effect is appreciable at the scale of the problem.

The student should also know why it barely affects a short motion on the Earth but does affect hurricanes.

Recommended learning route

1. Definition of the Coriolis Force: defines the Coriolis force, its direction relative to the relative velocity and the axis, and its value.
2. Applications of the Coriolis Force: analyzes its effect on the atmosphere, ocean currents, the path of long-range projectiles and rotating devices.

Physical criterion to acquire

The essential criterion is to estimate the order of magnitude first: the force is small unless the relative velocity or the time is large. It is included only if the deflection it produces is comparable to the precision sought, and always with the correct direction according to the hemisphere and the direction of motion.

Connection with real problems

• atmospheric circulation, hurricanes and winds.
• ocean currents.
• long-range ballistics.
• gyroscopes and rotating devices.

Final goal of the topic

The final goal is to compute the Coriolis force, determine its direction and judge whether it is relevant in a specific situation.