Chapter 11: Rotational Dynamics and Static Equilibrium
Applications



Life In A Moving Frame: THE CORIOLIS EFFECT

What Is The Coriolis Effect?

The Coriolis Effect, named after a 19th century French mathematician, describes the observed motions of objects whose positions are recorded in a rotating coordinate system. These effects include curved trajectories and action-reaction force pairs that show up in such accelerated systems.

Consider the situation schematically illustrated in the diagram on the left. Imagine two people sitting on a rotating platform. The people are represented by the red and the green dots. We are looking down at the platform which is rotating clockwise beneath us. Relative to a X-Y coordinate system on the ground, the red dot has a tangential velocity in the positive y-direction, the blue dot has a tangential velocity in the positive x-direction.

Suppose that at the instant depicted in the diagram the person in red is instructed to throw a ball in such as a way that the person in blue could catch it a quarter of a period later, i.e. when his location would be where the white dot is now. In the ground-based frame of reference the ball has a y-velocity as indicated by the black arrow in the vector diagram. The blue person has to throw the ball in the direction indicated by the blue vector. As a result the ball will start with an initial velocity represented by the red vector in the velocity vector diagram. The magnitude of the resultant velocity has to equal the distance between the blue dot and the white dot, divided by the quarter period of rotation of the platform.

What would the path of the ball look like, as recorded in a coordinate system attached to the platform?

The two pictures below are taken from a video recording of an event similar to the ball throw described above. The first image is the instant the boy in yellow throws the ball across the merry-go-round. The second image is the later instant when the boy in red catches the ball (at his new location.)

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throw Catch
From the point of view of the ground-based coordinate system, to reach the boy in red, the ball had to travel along a path marked by the yellow dots in the left picture below. To the observers riding on the merry-go-round, the path of the ball was not straight at all. The ball appeared to move as in the picture on the right. The boy in yellow threw the ball somewhat to his right. The ball then followed a curved path to land in hands of the boy in red.
 
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Path in Ground System Path in Rotating System
The merry-go-round video is available for view from a server at the Department of Atmospheric Sciences, University of Illinois Urbana-Champaign.

Are Coriolis Effects Real?

Maps attached to the spinning earth are rotating frames of reference. If you impart a northward initial velocity to a missile launched at the equator, the missile will not move along the meridian. The meridian on the map is rotating with the spinning earth. Referenced to this the earth-based the missile will follow a curved path. This is a real effect that has to be dealt with if the missile is to reach the target successfully.
Next, consider a train traveling on a track laid due north. To maintain a course due north, the east-west velocity of the train has to be changing constantly. The tracks have to exert a force on the train. The reaction force of the train will cause the tracks to wear more on one side than on the other. Similarly, rivers will carve out one more than the other? The left bank or the right bank? That depends on the direction of the flow (away from or towards the equator) and on the hemisphere.

The earthly weather is carried by the winds. These are driven by temperature and pressure differences in the atmosphere. The air is pushed from regions of high pressure to regions of low pressure. As the air masses move from one latitude to another, the Coriolis effect causes their paths to curve. Thus instead of moving directly into the low pressure regions, wind masses will circle them, forming vortices called cyclones in the northern hemisphere and typhoons in the southern hemisphere (as depicted in the image from NASA.)

Further study links: links:

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Further Study Questions:

1.  

Suppose you stand on a spot at the equator and decide to straight up, along the vertical (the line defined by the earth's gravity.) When you landed again, would you land at the same spot? Further East? West?

2.  

A river is flowing due north in the Northern Hemisphere. Which river bank, the east or the west, would you expect to show more erosion due to the Coriolis effect?

3.  

Flushing a toilet or emptying a bathtub causes the outflowing water to form a vortex. Is that a Coriolis Effect?

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