When physics studies the process of motion of bodies in non-inertial frames of reference, one has to take into account the so-called Coriolis acceleration. In the article we will give it a definition, show why it occurs and where it manifests itself on Earth.
What is Coriolis acceleration?
To answer this question briefly, 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 frame of reference.
Recall that non-inertial systems move with acceleration or rotate in space. In most physical problems, our planet is assumed to be an inertial frame of reference, since its angular velocity of rotation is too small. However, when considering this topic, the Earth is assumed to be non-inertial.
There are fictitious forces in non-inertial systems. From the point of view of an observer in a non-inertial system, these forces arise without any reason. For example, centrifugal force isfake. Its appearance is not caused by the impact on the body, but by the presence of the property of inertia in it. The same applies to the Coriolis force. It is a fictitious force caused by the inertial properties of the body in a rotating frame of reference. Its name is associated with the name of the Frenchman Gaspard Coriolis, who first calculated it.
Coriolis force and directions of movement in space
Having become acquainted with the definition of Coriolis acceleration, let us now consider a specific question - in what directions of movement of a body in space relative to a rotating system does it occur.
Let's imagine a disk rotating in a 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 opposes it, then the body will fly off the disk.
Now suppose that the body starts to move vertically upwards, that is, parallel to the axis. In this case, its linear speed of rotation around the axis will be equal to that of the disk, that is, no Coriolis force will arise.
If the body began to make a radial movement, that is, it began to approach or move away from the axis, then the Coriolis force appears, which will be directed tangentially 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 located ondifferent distances from the axis of rotation.
Finally, if the body moves tangentially to the rotating disk, then an additional force will appear that will push it either towards the axis of rotation or away from it. This is the radial component of the Coriolis force.
Since the direction of the Coriolis acceleration coincides with the direction of the considered force, this acceleration will also have two components: radial and tangential.
Formula of force and acceleration
Force and acceleration in accordance with Newton's second law are related to each other by the following relationship:
F=ma.
If we consider the example above with a body and a rotating disk, we can get 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 for the relationship between angular and linear velocity. In summary, the Coriolis force can be defined as follows:
F=-2m[ωv].
Here m is the mass of the body, v is its linear velocity in a non-inertial frame, ω is the angular velocity of the reference frame itself. The corresponding Coriolis acceleration formula will take the form:
a=-2[ωv].
The vector product of the speeds is in square brackets. It contains the answer to the question where the 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 studiedacceleration leads to a curvature of a rectilinear trajectory of motion.
Influence of the Coriolis force on the flight of a cannonball
To better understand how the studied force manifests itself in practice, consider the following example. Let the cannon, being at the zero meridian and zero latitude, shoot straight to the north. If the Earth did not rotate from west to east, then the core would fall at 0° longitude. However, due to the rotation of the planet, the core will fall at a different longitude, shifted to the east. This is the result of the Coriolis acceleration.
The explanation of the described effect is simple. As you know, points on the Earth's surface, together with air masses above them, have a large linear rotation speed if they are located at low latitudes. When taking off from the cannon, the core had a high linear speed of rotation from west to east. This speed causes it to drift eastward when flying at higher latitudes.
Coriolis effect and sea and air currents
The influence of the Coriolis force is most clearly seen in the example of ocean currents and the movement of air masses in the atmosphere. Thus, the Gulf Stream, starting in the south of North America, crosses the entire Atlantic Ocean and reaches the shores of Europe due to the noted effect.
As for air masses, the trade winds, which blow from east to west all year round in low latitudes, are a clear manifestation of the influence of the Coriolis force.
Example problem
The formula forCoriolis acceleration. It is necessary to use it to calculate the amount of acceleration that a body acquires, moving at a speed of 10 m / s, at a latitude of 45 °.
To use the formula for acceleration in relation to our planet, you should add to it the dependence on latitude θ. The working formula will look like:
a=2ωvsin(θ).
The minus sign has been omitted because it defines the direction of acceleration, not its modulus. For the Earth ω=7.310-5rad/s. Substituting all known numbers into the formula, we get:
a=27, 310-510sin(45o)=0.001 m/ c2.
As you can see, the calculated Coriolis acceleration is almost 10,000 times less than the gravitational acceleration.
