An elementary treatment of the theory of spinning tops and gyroscopic motion, by Harold Crabtree.

CHAPTER III. DISCUSSION OF THE PHENOMENA IESCRIBED IN THE INTRODUCTORY CHAPTER. 46. If we turn to the Introductory Chapter we shall now see the reasons for the paradoxical behaviour of the tops there described. To take the first instance mentioned if a top is placed on its toe while spinning, the torque, which would cause it to fall over if it were not spinning, fails in this case to turn over the axle but rotates it, and so the top precesses. Also, if we consider the rule given in Art. 38 for the direction of precession, we see why an ordinary top precesses in the direction of its spin, when viewed, say, from above (Fig. I.), while that in Fig. III. (a) precesses in the reverse direction: for in the latter case the centre of gravity is below the point of support and the torque acts in the reverse direction. 47. Let us now consider what causes a top that has been spun at an inclination to the vertical to rise to a more vertical (though not necessarily quite vertical) position before settling down to a steady motion. Suppose we take an ordinary top and spin it on a rough board. When it has settled down to a motion in which its axle is practically at a constant angle to the vertical, let us drag the board round in the same direction as the precession. It will be found that the centre of gravity of the top rises, and some of us may remember that the method of resuscitating a dying top is to get it on to one's hand and drag the hand round in the necessary direction. Similarly, if we draw the hand round in the opposite direction the top falls; so that we can sum up our experiment in the two following statements: (i) hurry the precession, the top rises; (ii) retard the precession, the top falls. Hence, when a top is spun at an inclination to the vertical and rises, there must be at first something that is hurrying the precession, and eventually (since the top afterwards falls) something that retards it.

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Title
An elementary treatment of the theory of spinning tops and gyroscopic motion, by Harold Crabtree.
Author
Crabtree, Harold.
Canvas
Page 47
Publication
London,: Longmans, Green, and co.,
1909.
Subject terms
Tops
Gyroscopes

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"An elementary treatment of the theory of spinning tops and gyroscopic motion, by Harold Crabtree." In the digital collection University of Michigan Historical Math Collection. https://name.umdl.umich.edu/abr4615.0001.001. University of Michigan Library Digital Collections. Accessed May 1, 2025.
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