Debunking Coriolis Force Myths

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  • Debunking Coriolis Force MythsAsif Shakur Citation: The Physics Teacher 52, 464 (2014); doi: 10.1119/1.4897580 View online: http://dx.doi.org/10.1119/1.4897580 View Table of Contents: http://scitation.aip.org/content/aapt/journal/tpt/52/8?ver=pdfcov Published by the American Association of Physics Teachers Articles you may be interested in Cyclone on a Turntable: Illustrations of the Coriolis Force Phys. Teach. 47, 546 (2009); 10.1119/1.3246477 Shallow water equations with a complete Coriolis force and topography Phys. Fluids 17, 106601 (2005); 10.1063/1.2116747 Coriolis Force on Your Arms Phys. Teach. 41, 516 (2003); 10.1119/1.1631619 Coriolis-effect demonstration on an overhead projector Phys. Teach. 37, 244 (1999); 10.1119/1.880248 Feeling forces that produce torques Phys. Teach. 36, 15 (1998); 10.1119/1.879948

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  • 464 The Physics Teacher Vol. 52, NoVember 2014 DOI: 10.1119/1.4897580

    lot faster than Joe. (The lot faster refers to linear speed in m/s. They have the same angular speed.) Now suppose Moe switches to track 3 but maintains the same linear speed he had on track 4. Then Joe and Moe will not stay in step. Moe will now get ahead and to the east of Joe. Continuing on with this analogy, if Moe now switches to track 2 while maintain-ing his track 4 speed, he will be even farther east of Joe.

    A similar scenario unfolds when an object is dropped at the equator from a high tower. The object on the tower is on track 4, so to speak, whereas the observer on the ground is on track 1 as depicted12 in Fig. 2. The dropped ob-ject retains its original horizontal component of velocity because it was dropped from a rotating Earth. This horizontal component of the dropped object does not change as it falls (almost) vertically. (Its initial vertical component of velocity is zero and increases as it falls). Just like the analogy of Moe switching to smaller tracks while retaining his original speed, the falling object keeps veering to the east. The closer it gets to the ground, the more it veers to the east.13

    Now the fun really begins with the second Coriolis force myth. Suppose that we throw an object up from the ground instead of dropping from the top of a tower. What will hap-pen now? You may think that going up it will veer to the west and coming back down, as before, it will veer to the east. So overall the object will fall back exactly from where it was launched vertically up. Once again, this intuitive conclusion is incorrect. The object in making the up and down trip veers to the west. It veers to the west going up and it also veers to the west coming down. In fact, it veers to the west four times as much as the object dropped from the tower veers east! Let us consider Joe and Moe again. This time it is Joe who moves to track 2 but keeps running at her slow linear track 1 speed. Obviously Joe will find herself west of Moe. If Joe now switches to track 3 (again maintaining her track 1 speed), she will veer even more west of Moe. Now what happens when Joe turns around and switches back to track 2 (again at her original track 1 speed)? Joe still keeps veering to the west! Similarly, the object thrown up keeps veering to the west go-ing up and coming down.

    Our object thrown up stays in air twice as long as the ob-

    Debunking Coriolis Force MythsAsif Shakur, Salisbury University, Salisbury, MD

    Much has been written and debated about the Co-riolis force.1-8 Unfortunately, this has done little to demystify the paradoxes surrounding this ficti-tious force invoked by an observer in a rotating frame of ref-erence. It is the purpose of this article to make another valiant attempt to slay the dragon of the Coriolis force! This will be done without unleashing the usual mathematical apparatus, which we believe is more of a hindrance than a help.

    Let us begin with an object dropped from the top of a tower at the equator. Earth rotates from west to east. A nave analysis of this scenario will lead to the first myth that the object dropped from the tower at the equator should appear to fall west of the vertical to an observer stationed on the rotating Earth, the nave reasoning being that the point di-rectly beneath the falling object on the Earth is moving away at a high speed. A more thoughtful analysis should reveal that Earth and the falling object are not independent enti-ties. They are inextricably intertwined by the force of gravity. Since the falling object is connected to Earth by gravity, it must move with Earth. Unfortunately, this thoughtful analy-sis will lead to the still incorrect conclusion that the falling object should fall vertically and not veer east or west of the vertical. This intuitive conclusion is incorrect. Experiments reveal that the object falls east of the vertical.9-11 An earth-bound observer finds this eastward deflection curious, and attributes it to a fictitious force known as the Coriolis force. So, then, why does an object dropped from a tower at the equator fall a few centimeters east of the vertical as verified by experiments? In order to answer this question, let us consider a simple analogy (Fig. 1).

    Fig. 1. Joe and Moe running clockwise on horizontal tracks 1 and 4, respectively.

    Josephine (Joe) on track 1 and Moses (Moe) on track 4 are running clockwise (west to east) as depicted in Fig. 1. In order for Joe and Moe to stay in step (so the two jogging partners can chit chat as they run), Moe will have to run a

    Joe on Track 1

    East West

    Moe on Track 4

    Fig. 2. Joe and Moe track projection from hori-zontal to vertical for the tower drop.

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  • The Physics Teacher Vol. 52, NoVember 2014 465

    13. In our simple analysis, we ignored the fact that conservation of angular momentum requires that the horizontal component of the velocity increase as the object falls. This effect serves to increase the expected amount of eastward deflection only slightly.

    Asif Shakur (Doc) is a professor of physics at Salisbury University in Salisbury, MD. He obtained his PhD from The University of Calgary, Canada. He recently co-authored Bells Theorem and Quantum Realism, published by Springer (2012).AMSHAKUR@salisbury.edu

    ject dropped from the tower. But then why does it veer to the west four times as much instead of only twice as much? There is a subtle observation we need to make in order to qualita-tively and suggestively explain this factor of four. Recall that the object dropped from the top of the tower veers east most when it is close to the ground (just like Moe veers to the east of Joe most when he is on track 2 rather than track 3).

    However, our object dropped from the top of the tower is moving fastest (vertically speaking) at this time and does not spend enough time veering to the east. The object thrown up veers to the west going up and also coming down. Moreover, the object thrown up veers to the west most when it is higher up where it is slowest (in the vertical direction) and also spends a lot more time veering to the west. This is an intuitive explanation of why an object thrown up veers to the west four times as much as an object dropped from the top of the tower veers east.

    Acknowledgment The author would like to thank the anonymous reviewer for providing Fig. 2 in order to transform the frame of reference from horizontal to the vertical tower.

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    ing object, Am. J. Phys. 52, 562 (June 1984).5. D. Sterling, Reply to Comment on The eastward deflection

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    9. A. French, The deflection of falling objects, Am. J. Phys. 52, 199 (March 1984).

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    11. E. Hall, Do objects fall south? Phys. Rev. 16, 246 (1903).12. Figure 2 switches the readers perspective from the horizontal

    track in Fig. 1 to a 90 rotation to a vertical plane. This corre-sponds to switching from the blue plane to the red plane in Fig. 2. The top of the tower corresponds to track 4 and the bottom of the tower, on the surface of Earth, corresponds to track 1. The height of the tower is very small compared to the radius of Earth. Nonetheless, sensitive experiments have successfully measured the eastward deflection of falling objects.

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