# What is Coriolis force: Definition and 76 Discussions

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 (or counterclockwise) 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 (non-accelerating) 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. The Coriolis force acts in a direction perpendicular to the rotation axis and to the velocity of the body in the rotating frame and is proportional to the object's speed in the rotating frame (more precisely, to the component of its velocity that is perpendicular to the axis of rotation). The centrifugal force acts outwards in the radial direction and is proportional to the distance of the body from the axis of the rotating frame. These additional forces are termed inertial forces, fictitious forces or pseudo forces. By accounting for the rotation by addition of these fictitious forces, Newton's laws of motion can be applied to a rotating system as though it was an inertial system. They are correction factors which are not required in a non-rotating system.In popular (non-technical) usage of the term "Coriolis effect", the rotating reference frame implied is almost always the Earth. Because the Earth spins, Earth-bound observers need to account for the Coriolis force to correctly analyze the motion of objects. The Earth completes one rotation for each day/night cycle, so for motions of everyday objects the Coriolis force is usually quite small compared with other forces; its effects generally become noticeable only for motions occurring over large distances and long periods of time, such as large-scale movement of air in the atmosphere or water in the ocean; or where high precision is important, such as long-range artillery or missile trajectories. Such motions are constrained by the surface of the Earth, so only the horizontal component of the Coriolis force is generally important. This force causes moving objects on the surface of the Earth to be deflected to the right (with respect to the direction of travel) in the Northern Hemisphere and to the left in the Southern Hemisphere. The horizontal deflection effect is greater near the poles, since the effective rotation rate about a local vertical axis is largest there, and decreases to zero at the equator. Rather than flowing directly from areas of high pressure to low pressure, as they would in a non-rotating system, winds and currents tend to flow to the right of this direction north of the equator (anticlockwise) and to the left of this direction south of it (clockwise). This effect is responsible for the rotation and thus formation of cyclones (see Coriolis effects in meteorology).
For an intuitive explanation of the origin of the Coriolis force, consider an object, constrained to follow the Earth's surface and moving northward in the northern hemisphere. Viewed from outer space, the object does not appear to go due north, but has an eastward motion (it rotates around toward the right along with the surface of the Earth). The further north it travels, the smaller the "diameter of its parallel" (the minimum distance from the surface point to the axis of rotation, which is in a plane orthogonal to the axis), and so the slower the eastward motion of its surface. As the object moves north, to higher latitudes, it has a tendency to maintain the eastward speed it started with (rather than slowing down to match the reduced eastward speed of local objects on the Earth's surface), so it veers east (i.e. to the right of its initial motion).Though not obvious from this example, which considers northward motion, the horizontal deflection occurs equally for objects moving eastward or westward (or in any other direction). However, the theory that the effect determines the rotation of draining water in a typical size household bathtub, sink or toilet has been repeatedly disproven by modern-day scientists; the force is negligibly small compared to the many other influences on the rotation.

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1. ### I Exploring the Coriolis Force: Real or Imagined?

Is the Coriolis force actually experienced by an object, or is the object simply deflected in its path?

3. ### Coriolis Force in East-West Direction

For objects traveling north or south, the Coriolis force makes sense. The velocity of the Earth's surface changes with latitude, causing an object to drift east or west relative to the Earth's surface. However, when an object is traveling east or west, the latitude is not changing. How would...
4. ### Understanding the Coriolis Force: How to Calculate It

I know that the perpendicular force is the Coriolis force, but I don't know how to get it
5. ### Coriolis Force and Centrifugal Force

Hello! So for a) I have done the following m = 400t = 400000 kg v = 300 km/h = 83,3 m/s ##\alpha## = 50 (degrees) Now this is the formula for the Coriollis effect $$F = 2 \cdot m (v × \omega)$$ So in a book I found in the library regarding physics I've found a similar example that used...
6. ### Motion of particles close to the Earth

I tried to solve the problem in 2 ways, first using lagrangian mechanics and second by putting a rotating reference frame on the initial take-off point. However I cannot be sure if the equations of motion for the two solutions came out the same. A-) Equations of motion from Lagrangian...
7. ### Gyroscope (Coriolis Torque and Force)

I know that to prove the total coriolis torque from the coriolis torque on a point mass is to express dm as a function of ##d\theta## and integrate from 0 to ##2\pi## and then the x component disappears due to orthogonality of sine and cosine. But i am stuck at other parts.
8. ### Direction of the Coriolis force

How can I determine direction of Coriolis force for these cases?1)Ship travel at 45th north parallel to the east (course 90°)2)Ship travel at north hemisphere at course 45°3)Ship travel at equator at east (course 90°) My attempt: 1) Coriolis force is point up,vertical to the Earth surface 2)I...
9. ### Coriolis force caused by tangential velocity

From another recent thread I learned that you see a Coriolis force if an object in a rotating reference frame moves along a tangent at some velocity v. (I was already familiar with the case where the velocity is radial). I still find it a little counter-intuitive that the force has the same...
10. ### Two boys on a merry go round

This is a tipical Coriolis effect example, and I know what the trajectory drawn by the ball looks like from the perspective of B, and from the perspective of someone outside. But the acceleration with respect to ##B## is 0, isn't it? Because the problem says "the ball has no horizontal...
11. ### Does the Coriolis force act on the propagation of light?

Summary: Robert Sungenis explains the sagnac effect Robert Sungenis, a well-known proponent of geocentrism, has authored a https://gwwdvd.com/what-allows-the-sun-to-revolve-around-the-earth/ in which he tries to explain the Sagnac effect as a result of Coriolis force (p.16-17), which he thinks...
12. ### How Does the Coriolis Force Affect Particle Motion in a Rotating System?

m = Particles mass, Omega = Systems angular frequency, v' = particles velocity. Attempt at a Solution: $$F_{C} = -2m \bar{\omega} \times \bar{v}^{'} = -2 \bar{\omega} \times \bar{p} = 2 \bar{p} \times \bar{\omega}$$ Let  \bar{\omega} = \frac {\bar{r} \times \bar{v}} {r^2}, \alpha = \frac...
13. ### I Coriolis force, real or just an illusion?

So does then huricans really rotate or just appear to rotate? Does wind particles in huricane feel centrifugal force because they move in curved path or maybe not because they actually go in straight line? I never understand coriolis force 100%,is wind particles really rotate or this is just...
14. ### Torque about center of mass due to Coriolis force, is it 0?

It’s essentially a question about cross product identities. I want to analyze a problem in a frame of reference which is rotating with angular velocity ##\vec \Omega## relative to an inertial frame. In this non-inertial frame, we have a rigid body rotating with constant angular velocity ##\vec...
15. ### Coriolis force and the Earth's rotation

Homework Statement A body is thrown as shown in the picture (0°<x<90°). In what direction the body will the body move in relation to the point it was thrown from - east or west (assume the distance between the point the body was thrown from and the point it lands at is no more than a few...
16. ### I Conceptual question about the Coriolis force and the weather

Dear all, there is something bugging me for a while now, and it's about a favourite topic of confusion: the Coriolis-force! A fictitious force is a force which disappears if you transform to an inertial frame. At the algebraic level I have a good understanding of this, I think (Newton's 2nd...
17. ### Problem with Coriolis Acceleration

Homework Statement Find the magnitude in g's of the Coriolis acceleration due to the Earth's rotation of a plane flying 600 mph due north over the location of latitude (37˚13'04"N), longitude (121˚50'39"W), at an elevation of 80 meters above mean sea level. Homework Equations aCor = 2Ω × vxy...
18. ### Dynamic reaction versus Coriolis acceleration of the disk

<< Thread moved from the technical forums, so no Homework Help Template is shown >> I have mind boggling problem, trying to distinguish between Dynamic reaction versus Coriolis acceleration of thin hoop. Problem: A thin, hoop of mass m and radius r spins at the constant rate ω 1 about an axle...
19. ### I Space elevator and Coriolis force

It seems to me that the concept of a space elevator does not take Coriolis force into account. If the elevator were in built with a space station in geosynchronous orbit and counterweight then there is more to reaching the space station than just climbing the rope. The rope would have to be...
20. ### Question about the Coriolis effect

Homework Statement It's a question about the deviation of a bullet fired on Earth's surface: **I solved the question, but I can't figure out what exactly this deviation means, where is it on the following question's picture: The problem: A bullet is fired from a gun towards a target at...
21. ### The Coriolis Force: Where Will It Take You?

Homework Statement A plane is flying in latitude 25S to the west. due to the Coriolis force will he fly to the southern pole or to the equator? and the same question but that he is flying to the west in 25N? Homework EquationsThe Attempt at a Solution I'm not sure, but think that Coriolis...
22. ### B What Causes a Particle to Move in a Circular Trajectory Due to Coriolis Force?

Hello, I got a question about the coriolis force. It is probably super simple, but I am still not getting it: The coriolis force, forces my particle onto a circle trajectory, but I am not sure why (yes, I can show it mathematically, but I want to understand what is happening). When I am moving a...
23. ### I Consider Coriolis force or not?

Hello, my question is very short. I have a spinning bar, with a small ring threaded. I know that for analyzing the problem I have to consider the centrifugal force that makes the small ring go away from the center. My question is do I have to also consider the coriolis force? : - 2m (w x v'), or...
24. ### Coriolis Force on a Race Car at 45 Degrees North

Homework Statement Find the magnitude and direction of the Coriolis force on a racing car of mass 10 metric tons traveling due south at a speed of 400km/hr at a lattitude of 45 degrees north. Homework Equations F_{cor}=-2m\omega\times v The Attempt at a Solution \omega=2\pi/(24*3600 \quad...
25. ### I Reconciling the Coriolis Force Contradiction on a Spinning Disk

Imagine there is a frictionless disk that spins with angular speed w. There is a ball on it that sits motionless at some radius r from the center. Now, switch to the frame of the rotating disk. In this frame the ball should be spinning with speed w * r. Edit: To be clear, the ball is NOT moving...
26. ### Understanding Coriolis Force in a Rotating Pipe

Homework Statement Homework Equations https://wikimedia.org/api/rest_v1/media/math/render/svg/1a061d2667e5d9f69dc385e359e7260a3eb1deff https://wikimedia.org/api/rest_v1/media/math/render/svg/ba88069934aa8abb2a2466f84121f385e6e8971f The Attempt at a Solution I have solved equation for r(t) and...
27. ### Coriolis Force Across the Equator

Homework Statement A fast sprinter with a mass of 80 kg runs across the equator. What is the value of the Coriolis force he experiences? Homework Equations F=ma a=2ωVradial ω=7.27 x10-5 rads-1 Earth rotates from west to east. The Attempt at a Solution I pick a direction of travel - South to...
28. ### Coriolis force in rotating space station

There is a car driving with speed u opposite the direction of the rotation of the space station. ω=√(g/R) so artificial Earth gravity at R. Resulting tangential speed of station is v=√(gR) and centrifugal force is therefore mg radially out. Coriolis force is 2muxω radially in, magnitude...
29. ### Angular momentum conservation and constant velocity as expla

I'm confused about situations involving rotating frames in which the angular momentum is conserved and the initial velocity does not change. I'll make an example. Take a rotating carousel (constant angular velocity) with no friction on it and a ball. At the initial time instant the ball has the...
30. ### Coriolis force and conservation of angular momentum

I'm trying to understand the relations between the existence of Coriolis force and the conservation of angular momentum. I found this explanation on Morin. I do not understand the two highlighted parts. In particular it seems that Coriolis force is there to change the angular momentum of the...
31. ### Coriolis effect causes in motion of a free falling object

I don't understand what are the causes of the Coriolis effect for objects moving with respect to Earth. For istance consider an object free falling on the Earth from an height h. Its tangential velocity its greater than the velocity of an object on the surface of Earth, hence it moves eastward...
32. ### Polar Jet Stream Flow: Counter-Clockwise Around Earth

Why does the polar jet stream flow counter-clockwise around the Earth (as viewed from the north pole)? It seems that since the air at the north end of the Ferrel Cell and the south end of the Polar Cell rises, the Coriolis effect would cause a circulation in the clockwise direction.
33. ### What is the direction of the Coriolis force in various scenarios at the equator?

Homework Statement 4) Find the direction does the Coriolis force in the following case a) a jet going north over the equator; b) a rocket going up at the equator; c) a pendulum at the equator viewed from above (please give the rotational direction.) d) a rocket going up at the south pole...
34. ### Coriolis Force on a Playground

Homework Statement Four children are playing toss on a merry-go-round which has a radius of r=2m. The merry-go-round turns counterclockwise and completes one revolution in 2 seconds. The child who has the ball wants to toss it to its right neighbour. It tosses the ball towards the center of the...
35. ### Coriolis Force Along the Surface of the Earth

Homework Statement I don't want to post the actual question because I want to understand the situation in a general case. Basically, there is a bullet that moves south along the surface of the Earth as in this diagram: http://abyss.uoregon.edu/~js/images/coriolis_effect.gif. You have to find...
36. ### Train experiencing Coriolis force

Homework Statement A train at latitude λ in the northern hemisphere is moving due north with a speed v along a straight and level track. Which rail experiences the larger vertical force? Show that the ratio R of the vertical forces on the rails is given approximately by: R= 1+ 8Ωvh sin λ / ga...
37. ### Classical Mechanics: Coriolis Effect Problem

Homework Statement A bird of mass 2 kg is flying at 10 m/s in latitude of 60° N, heading due East. Find the horizontal and vertical components of the Coriolis force acting on it. Homework Equations The Coriolis Force, F = 2mw∧v. Where ∧ shows the cross product between angular frequency...
38. ### Coriolis Force and the Earth's Rotation,

/* Last year, in first year I had problems with understanding the Coriolis Force. I asked the lecturer about it and he found a simpler way of explaining it. I thought I had understood. However, I've spent many hours this weekend trying to understand it and it keeps eluding me. That explanation...
39. ### Understanding the Coriolis Force

I'm having a little trouble understanding why the Coriolis force is proportional to the velocity vector of the object in the rotating frame. It seems to me if you had a spinning cd for example and let a ball go on it, if the ball was moving slower from the inside to the outside it would divert...
40. ### Coriolis Force & Rotating Body Problem

Homework Statement Coriolis Force - Explain how the following situations would appear in both the inertial and non-inertial reference frames. Assume the inertial frame to be a view from above. Situation 1 - a ball is thrown from the centre of a merry-go-round which is rotating...
41. ### What is the Effect of Coriolis Force on Rotating Frames of Reference?

Definition/Summary Coriolis force is a non-physical force, appearing, like centrifugal force, only in rotating frames of reference. It is an inertial force, like centrifugal force and gravity, meaning that it affects all matter, proportionately to its mass (inertia), but independently of...
42. ### Coriolis Force, Motion of projectile

I've been wonder something about coriolis force. Well... when we consider motion of projectile on earth, we have to consider coriolis force due to Earth's rotation and we know that coriolis force varies with latitude. In the book (fowles's) they set differential equation and just...
43. ### Archived Centripetal force and Coriolis force?

Homework Statement Suppose that you are on a rotating platform, going around with frequency w a distance r from the center. Suppose that you are watching an object that moves in a straight line. Produce an animation that shows the position of the object from your perspective. Does this...
44. ### Coriolis Force on a Wheel of radius r spinning at angular velocity

Imagine that we have a wheel spinning with the axis of rotation normal to the Earth's surface. For convenience, let's assume that the wheel is located somewhere in the north hemisphere. According to the definition of the Coriolis force, every little particle dm of the wheel has a coriolis...
45. ### Coriolis force of a stone throw

Homework Statement A stone is left to fall from a 80 meters high tower on the equator. How far in front of the tower it will fall. Homework Equations The angular velocity of the earth: ω=7.27E-5 [rad/sec] It reaches the ground in 4 seconds. The Attempt at a Solution This problem is solved, in...
46. ### Coriolis force - Question about sign

Dear all I have a question concerning the Coriolis acceleration expression. I learned it as Ac = -2ω x v, where ω is the vector which indicates the rotation axis direction of Earth and v the velocity of a body that I want to check the Coriolis effect on. My question: where the minus...
47. ### Coriolis force thought experiment

Let's say I build a 500 m long circular road around the north pole. Then I drive on the road at speed 20 m/s, to the east. There will be a noticeable inertial force to the south. Is that inertial force a Coriolis force?
48. ### What is the Coriolis Force and How Does it Affect Driving Direction?

I read that in the northern hemisphere the Coriolis force is always 90 degrees to the right of the vector of motion in the rotating frame. That is, driving from SF to NY there is a force to the south, driving from NY to SF there is a force to the north. OK, pseudoforce, whatever. I don't...
49. ### Coriolis force could generate currents?

Let`s say we have rotating body in the space which is covered completely or partially with some liquid.For example water.Rotating body do not exibits gravitational or tidal interation with other bodies.Will Coriolis force generate some constant currents in liquid or not? Please answer if you...
50. ### Circular Motion Due to Coriolis Force

Homework Statement A particle has velocity v on a smooth horizontal plane. Show that the particle will move in a circle due to the rotation of the Earth and find the radius of the circle. (Ignore all fictitious forces except the Coriolis force.) Homework Equations Coriolis force, given by...