When the physics of the motion of bodies in non-inertial reference systems is studied in physics, the so-called Coriolis acceleration must be taken into account. In the article we will give him a definition, show why it occurs and where it appears on Earth.
What is Coriolis acceleration?
Briefly answer this question, we can say that this is the acceleration that occurs as a result of the action of the Coriolis force. The latter manifests itself when the body moves in a non-inertial rotating reference frame.
Recall that non-inertial systems move with acceleration or rotate in space. In most physical problems, our planet is assumed to be an inertial reference system, because its angular velocity of rotation is too low. However, when considering this topic, the Earth is considered non-inertial.
In non-inertial systems there are fictitious forces. From the point of view of an observer in a non-inertial system, these forces arise without any reason. For example, centrifugal force is fake. Its appearance is caused not by the effect on the body, but by the presence of its inertia properties. The same applies to the Coriolis force. It is a fictitious force caused by the inertial properties of the body in a rotating reference frame. Its name is associated with the name of the Frenchman Gaspard Coriolis, who first calculated it.
Coriolis force and direction of movement in space
Having become acquainted with the definition of Coriolis acceleration, we now consider a specific question - in which directions of the body's movement in space relative to the rotating system it arises.
Imagine a disk rotating in the horizontal plane. A vertical axis of rotation passes through its center. Let the body rest on the disk relative to it. At rest, a centrifugal force acts on it, directed along the radius from the axis of rotation. If there is no centripetal force that counteracts it, then the body will fly off the disk.
Now suppose that the body began to move vertically upward, that is, parallel to the axis. In this case, its linear speed of rotation around the axis will be equal to that for the speed of the disk, that is, no Coriolis force will arise.
If the body begins to make a radial movement, that is, it begins to approach or move away from the axis, then the Coriolis force appears, which will be tangential to the direction of rotation of the disk. Its appearance is associated with the conservation of angular momentum and with the presence of a certain difference in the linear velocities of the points of the disk, which are at different distances from the axis of rotation.
Finally, if the body moves tangentially to the rotating disk, an additional force will appear, which will push it either to the axis of rotation or away from it. This is the radial component of the Coriolis force.
Since the direction of Coriolis acceleration coincides with the direction of action of the considered force, this acceleration will also have two components: radial and tangential.
Power and Acceleration Formula
Force and acceleration in accordance with the second Newtonian law are related to each other by the following relationship:
F = m * a.
If we consider the example above with a body and a rotating disk, we can obtain a formula for each component of the Coriolis force. To do this, apply the law of conservation of angular momentum, as well as recall the formula for centripetal acceleration and the expression of the relationship of angular and linear velocity. In summary, Coriolis force can be defined as follows:
F = -2 * m * [Ο * v].
Here m is the mass of the body, v is its linear velocity in a non-inertial system, Ο is the angular velocity of the reference system itself. The corresponding formula of Coriolis acceleration will take the form:
a = -2 * [Ο * v].
In square brackets is the vector product of speeds. It contains the answer to the question of where Coriolis acceleration is directed. Its vector is directed perpendicular to both the axis of rotation and the linear velocity of the body. This means that the acceleration under study leads to a curvature of the rectilinear motion path.
Influence of Coriolis force on cannonball flight
In order to better understand how the studied force manifests itself in practice, consider the following example. Let the gun, being at the zero meridian and zero latitude, perform a shot strictly to the north. If the Earth did not rotate from west to east, then the core would fall at a longitude of 0 Β°. However, due to the rotation of the planet, the core will fall at another longitude, shifted to the east. This is the result of Coriolis acceleration.
The explanation of the described effect is simple. As you know, points on the surface of the Earth, together with the air masses above them, have a large linear speed of rotation, if they are in low latitudes. When leaving the cannon, the core had a large linear speed of rotation from west to east. This speed leads to its eastward displacement when flying at higher latitudes.
Coriolis effect and sea and air currents
The influence of the Coriolis force is most clearly traced on the example of ocean currents and on the movement of air masses in the atmosphere. Thus, the Gulf Stream, starting in southern North America, crosses the entire Atlantic Ocean and reaches the shores of Europe due to the noted effect.
As for the air masses, the trade winds are a striking manifestation of the influence of the Coriolis force, which blow from east to west all year round in low latitudes.
Task example
The formula for Coriolis acceleration was written above. It is necessary to use it to calculate the magnitude of the acceleration that the body acquires, moving at a speed of 10 m / s, at a latitude of 45 Β°.
To use the formula for acceleration as applied to our planet, we should add the dependence on latitude ΞΈ to it. The working formula will look like:
a = 2 * Ο * v * sin (ΞΈ).
The minus sign was omitted because it determines the direction of acceleration, and not its modulus. For the Earth, Ο = 7.3 * 10 -5 rad / s. Substituting all the known numbers in the formula, we get:
a = 2 * 7.3 * 10 -5 * 10 * sin (45 o ) = 0.001 m / s 2 .
As you can see, the calculated Coriolis acceleration is almost 10,000 times less than the gravitational acceleration.