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PAPERS| July 01 2014
William Case;
William Case a)
Department of Physics, Grinnell College
, P.O. Box 805, Grinnell, Iowa 50112
Search for other works by this author on:
Sahar Jalal
Sahar Jalal
Department of Physics, Grinnell College
, P.O. Box 805, Grinnell, Iowa 50112
Search for other works by this author on:
Am. J. Phys. 82, 654–658 (2014)
A rattleback is a canoe-shaped body that, when spun on a smooth surface, rotates stably in one direction only; when spun in the reverse direction it oscillates violently (i.e., it “rattles”) and reverses its direction of spin. This behavior can be traced to the misalignment of the principal axes of the body with respect to the symmetry axis of its bottom surface. Although analyses of the phenomenon exist in the literature, there is not a clear, direct presentation of the basic mechanism responsible for the reversal of direction. The goal of this paper is to present, as clearly as possible, a treatment of the phenomenon by focusing on the geometry of the usual rattleback. Two initial conditions are considered: rotation about the vertical axis with no oscillation, and oscillation about a horizontal axis with no rotation. For the first initial state, oscillatory motion about the two horizontal axes is analyzed using a combination of linearization and reasonable assumptions. The reversal is then analyzed using energy considerations. The analysis for the second initial state is more direct and elementary. In combination, these analyses explain the transitions from rotation to oscillation to rotation in the opposite direction. The non-reversal for the rotation opposite initial rotation is also accounted for. We also comment on how the rattleback might be modified allowing it to reverse in both directions and thus to repeatedly reverse its direction of rotation.
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Here by “usual” we refer to the most common rattleback. These are available from Educational Innovations, <teachersource.com>, as well as other vendors. A quite delightful rattleback referred to as a “Russian rattleback” is available from Grand Illusions Ltd., <www.grand-illusions.com/>. For this rattleback the mass distribution can be altered by rotating two toy turtles located near the opposite ends. The behavior of this rattleback is also well described by our treatment.
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, one might expect to find an extra term in Eq. (30) involving the cross product of the velocity of the center-of-mass and the velocity of the contact point P. Since these two velocities are both in the horizontal plane and we are interested only in the y-component of the angular momentum we may drop such a term.
© 2014 American Association of Physics Teachers.
2014
American Association of Physics Teachers
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