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## Hot answers tagged coriolis-effect

15

Ok, here is my (hopefully rigorous) demonstration of the origin of these forces here, from first principles. I've tried to be pretty clear what's happening with the maths. Bear with me, it's a bit lengthy! Angular velocity vector Let us start with the principal equation defining angular velocity in three dimensions, $$\dot{\vec{r}} = \vec{\omega} \times ... 13 The whirl is due to the net angular momentum the water has before it starts draining, which is pretty much random. If the circulation were due to Coriolis forces, the water would always drain in the same direction, but I did the experiment with my sink just now and observed the water to spin different directions on different trials. The Coriolis force is ... 10 The answer: the ball appears to be deflected ~10 cm. The calculation: For simplicity, say we tee off at the north pole. The effects are a bit weaker at more typical locations, you multiply by sin(latitude) = 0.64 for a 40 degree (central california or washington DC) latitude. The Coriolis effect exists because the Earth rotates while the ball is in ... 5 Since you want to explain it to your daughter, take a plastic bottle, cut the bottom open, turn it upside town, hold the top closed and fill it with water. Give her that bottle and have her release the top (which is on the bottom now, sorry for the bad phrasing). The water will whirl in different orientations whenever you repeat this (if it whirls at all) ... 5 The Coriolis acceleration goes like -2\omega \times v, which for the sake of an order of magnitude estimate we can take to be a\sim \omega v. But in order to get an observable effect, we don't just need an acceleration, we need a difference in acceleration between the two ends of the tub, which are separated by some distance L\sim 1 m. The ... 4 Firstly, is that correct? Yes your intuitive understanding for this part of the Coriolis effect is correct. The second part, that is, why wind in the East direction is deflected South, is a bit trickier, and involves the use of centripetal force. this is given by the equation: F = \frac{mv^2}{r} If we re-arrange the above equation, we can find ... 4 An alternate derivation for a due-north ball, ignoring the diminishing effect of latitude, that confirms Kevin's order of magnitude: Acceleration due to the Coriolis effect: a_C = -2 \, {\Omega \times v} \Omega = 2 \pi/day v = 45 m/s a_C = -0.00654498469 m/s^2 Horizontal displacement d is given by d = 1/2a_C\,t^2  Using earlier estimate of ... 3 Coriolis force is not an actual force, but rather an effect observed in rotating frame of reference. The light path is not actually bent, so it doesn't matter that the photon has no mass, the Earth's rotation will have an affect on the photon's apparent path. This does not contradict your calculation of F_{Coriolis}=0, because you have to put this force ... 3 could the Coriolis effect on snowing be so dramatic...? No. The Coriolis effect is only noticeable for objects traveling long distances with respect to Earth's surface for significant periods of time. For example, a ballistic missile fired hundreds of miles or a hurricaine that is hundreds of miles in diameter and lasts for days. Across the street is ... 3 The Coriolis force on the equator indeed does point outwards, if you are moving west to east. This is not the same as the centrifugal force, because the centrifugal force is present always - even if you are not moving. But when you move (west to east), there is an additional force on top of the centrifugal force - the Coriolis force. If you travel east to ... 3 Well, there is a partial yes that is a direct result of the Coriolis force: If you go up in a hot air balloon, you will be subject to various winds which will move you. And these winds are a result of the Earth spinning. In principle you should be able to navigate to most places on the globe by choosing height etc. in reality it is much too complex to do ... 3 The whirl happens in the draining tube, whose optimal solution to drain the bathtub is a laminar flow allowing for some rotation in the tube. What you see in the surface is the match between the solution of flow in the tube and the solution of flow in the surface. Angular momentum of the flow gets modified a lot as the tube twists and twists, sometimes even ... 2 I am not particularly an expert either, but my understanding is that shuttle flight is a very active process compared to ballistic motion, so any effects the Coriolis effect might have can just as well be considered as additional errors in the trajectory, which is being adjusted. There's an active feedback loop at work: "observe flightpath -> identify ... 2 You can think about it like this: It takes one day for the earth to perform a full rotation (about 86k seconds), on the other hand, it takes a few seconds for your sink to drain (lets say 10 seconds). So it takes 8600 times longer for the earth to do a full rotation than it takes the water to drain down the sink. It is not too hard to imagine that the ... 2 Rockets lean as they climb on purpose, in order to obtain the high orbital velocities needed to stay in space once they get there. For a nice explanation, see Orbital Speed at xkcd what-if, but the gist is the following. Being in orbit means going so fast that the Earth begins to curve away from you as you fall down towards it. The classic image to keep in ... 2 The Coriolis effect cannot possibly account for this. Other factors (e.g the shape of the basin and initial conditions for the water flow) should have a comparatively huger effect. This is intuitively obvious---if you are not convinced you should perform an experiment. Could be fun! You could also estimate characteristic scales (via dimensional analysis) ... 2 Well, first we know that the Coriolis force acting on the scale of a toilet is going to be a pretty small force. So the question can generally be tackled in the following way: Estimate the magnitude of the Coriolis force on the toilet water. Use this to estimate the magnitude of effect of the Coriolis force on the toilet water spin. Enumerate the ... 2 The rotation of your coordinate system causes the Coriolis effect. Things move in straight lines, but if your coordinate system is rotating, then the straight lines look curved from the perspective of your coordinate system. If you want to insist that objects move in straight lines in your coordinate system, then you must invent a fictitious reason why ... 2 Surprisingly, the answer is that yes you do, though the effect is very small. To see this consider the following (highly exaggerated) diagram of the lift shaft: The Earth rotates at a constant angular velocity of one rotation every 24 hours (\omega = 7.27 \times 10^{-5} radians/sec). The tangential velocity of a part of the lift shaft at a distance r ... 1 You are right: the coriolis effect in the equator is converted to a kind of centrifugal force. But in many situations only the horizontal Coriolis forces are accountes, because in the vertical one the gravity is so much greater. The vertical coriolis and the centrifugal force may point parallel, but they are still different forces. Let's think of a ... 1 If you project the velocity of a water parcel traveling up the channel into radial coordinates in both the inertial frame (space frame) and the rotating frame of reference (earth frame) then I think the necessary effects will become apparent. In the earth's frame, the velocity is (use a ' to symbolize the rotating frame):$$\vec{v} = 0\cdot\hat{r}' + ...

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Ok, let's see if I get this right. The circumference of the equator is 24902 miles. The Earth rotates 360° in 86,164.098 seconds. This means the surface of the Earth moves 1525.96 ft/sec at the equator. Adding 1000 ft to the height give a circumference of 24903 miles. This means the lateral speed is 1526.03 ft/sec; a difference of about 0.87 inches/sec. It ...

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Your logic is right on, it's just your arithmetic that needs work. First, of course, you need to assume that everything happens in a vacuum. Air resistance will dominate any other effects for the sort of distances you have indicated. Also, let's assume (just to make calculations easier, that this takes place on the equator, at sea level. Earth's equatorial ...

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You're focusing on the centrifugal force. You forgot about the coriolis effect. Neither has much of an effect for an object dropped from the top of a tree, even a very, very tall tree. The first thing you need to realize is that "down" (the direction in which a plumb line points) is generally not toward the center of the Earth. That is only true at the ...

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I would say that some parts are unclear, but no, it's not "wrong". Consider the return flight from Miami to Alaska. It's in the northern hemisphere so the deflection should be to the right, but the "earth rotating underneath" theory would predict deflection to the left. The animations are not showing that the cause is "the earth rotating underneath". ...

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WRT the second paragraph: The inertial observer will see an object (the walker) moving in a fixed radius circle with a lower tangential (and thus lower angular) velocity, than was seen when the walker was not walking... This in turn would reduce the centripetal force required to keep the walker moving in his slower, fixed radius circle, and this would be ...

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They really aren't related. The Coriolis force is essentially conservation of momentum. Remember that the Earth is (roughly) 24,000 miles in circumference at the equator, and so everything "at rest" on the equator is moving eastward at 1,000 mph. Away from the equator the ground's eastward speed is slower, roughly  v_\text{east} = v_\text{equator} \cos ...

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Corirolis force is simply due to a moving frame of reference. If you were on a merry-go-round, and threw a ball, it would go straight in the fair-ground frame of reference, but because you see it go away from the direction you threw it, you might suppose it experienced a force. The earth spins, and because we don't suspect this, we attrit normal inertial ...

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According to Wikipedia: Because the Earth completes only one rotation per day, the Coriolis force is quite small, and 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. Such motions are constrained by the surface of ...

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Flatness here means that the vertical component of motion can be neglected, i.e., $Z \ll R$ where $R=\sqrt{x^2+y^2}$ is the horizontal displacement. To derive the equations of motion (without using the Lagrangian or Hamiltonian formalism which would be the most direct method here) just write down the total energy \$E = mgZ + m/2 \; (\dot{x}^2 + \dot{y}^2) = ...

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