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An assortment of spinning tops A tough gang of Spinning Tops.jpg
An assortment of spinning tops

A spinning top, or simply a top, is a toy with a squat body and a sharp point at the bottom, designed to be spun on its vertical axis, balancing on the tip due to the gyroscopic effect.

Contents

Once set in motion, a top will usually wobble for a few seconds, spin upright for a while, then start to wobble again with increasing amplitude as it loses energy (angular momentum), and finally tip over and roll on its side.

Tops exist in many variations and materials, chiefly wood, metal, and plastic, often with a metal tip. They may be set in motion by twirling a handle with the fingers, by pulling a rope coiled around the body, or by means of a built-in auger (spiral plunger).

Such toys have been used since antiquity in solitary or competitive children games, where each player tries to keep one's top spinning for as long as possible, or achieve some other goal. Some tops have faceted bodies with symbols or inscriptions, and are used like dice to inject randomness into games, or for divination and ritual purposes.

The ubiquity of spinning tops lends to the fact that the toy is used to name many living things such as Cyclosa turbinata , whose name comes from the Latin roots for spinning top.

History

Ancient Roman wooden spinning top, from Tebtynis (Egypt), dating from the 1st-3rd century CE 2447 - Museo archeologico di Milano - Trottola, da Tebtynis, sec. I-III d.C. - Foto Giovanni Dall'Orto, 1 feb 2014.jpg
Ancient Roman wooden spinning top, from Tebtynis (Egypt), dating from the 1st–3rd century CE

Origins

The top is one of the oldest recognizable toys found on archaeological sites. Spinning tops originated independently in cultures all over the world. [1]

Besides toys, tops have also historically been used for gambling and prophecy. Some role-playing games use tops to augment dice in generating randomized results; it is in this case referred to as a spinner.

Gould mentions maple seeds, celts (leading to rattlebacks), the fire-drill, the spindle whorl, and the potter's wheel as possible predecessors to the top, which he assumes was invented or discovered multiple times in multiple places. [2]

Color demonstrations with tops

A top may also be used to demonstrate visual properties, such as by James David Forbes and James Clerk Maxwell in Maxwell's disc (see color triangle). By rapidly spinning the top, Forbes created the illusion of a single color that was a mixture of the primaries: [3]

[The] experiments of Professor J. D. Forbes, which I witnessed in 1849… [established] that blue and yellow do not make green, but a pinkish tint, when neither prevails in the combination…[and the] result of mixing yellow and blue was, I believe, not previously known.

James Clerk Maxwell, Experiments on colour, as perceived by the eye, with remarks on colour-blindness (1855), Transactions of the Royal Society of Edinburgh
Large Tin Top with Sound Metallike Sboura me 'Ekho.jpg
Large Tin Top with Sound
Color top 1895.png
PSM V11 D687 The color top.jpg
Maxwell's color top (1895) and one from Popular Science Monthly (1877)

Maxwell took this a step further by using a circular scale around the rim with which to measure the ratios of the primaries, choosing vermilion, emerald, and ultramarine. [4]

Spinning methods

Finger twirling

Smaller tops have a short stem, and are set in motion by twirling it using the fingers. A thumbtack may also be made to spin on its tip in the same way.

Strings and whips

Extract from Children's Games (1560) Die Kinderspiele - Verschiedene Kreisel.jpg
Extract from Children's Games (1560)

A typical fist-sized model, traditionally made of wood with a blunt iron tip, is meant to be set in motion by briskly pulling a string or rope tightly coiled around the body. The rope is best wound starting near the tip and progressing up along the widening body, so that the tension of the string will remain roughly constant while the top's angular speed increases.

These tops may be thrown forward while firmly grasping the end of the string and pulling it back. The forward momentum of the top contributes to the string's tension and thus to the final spin rate.

In some throwing styles, the top is thrown upside-down, but the first loop of the rope is wound around a stubby "head". Then, the sudden yank on the head as the string finishes unwinding causes the spinning top to flip over and land on its tip.

Alternatively, tops of this class may be started by hand but then accelerated and kept in motion by striking them repeatedly with a small whip.

Augers

Some larger models are set in motion by means of a built-in metal auger (spiral plunger). In these models, the actual top may be enclosed in a hollow metal shell, with the same axis but decoupled from it; so that the toy may appear to be stationary but "magically" balanced on its tip.

Magnetic fields

Some modern tops are kept perpetually in motion by spinning magnetic fields from a special ground plate.

Notable types

Perinola plastico.jpg
A cheap plastic version of the perinola
Celt with weights of gemstone turtles-01.jpg
Carved wooden rattleback

Gould classifies tops into six main types : twirler, supported top, peg-top, whip-top, buzzer, and yo-yo. [5]

Modern tops may have several sophisticated improvements, such as a relatively sharp tip made of ruby or a hard ceramic like tungsten carbide, that reduces the friction with the ground surface. In addition, plastic and metal have largely supplanted the use of wood in tops.

Physics

A precessing gyroscope Gyroscope precession.gif
A precessing gyroscope

The motion of a top is described by equations of rigid body dynamics, specifically the theory of rotating rigid bodies.

Because of the small contact area between the tip and the underlying surface, and the large rotational inertia of its body, a top that is started on a hard surface will usually keep spinning for tens of seconds or more, even without additional energy input.

Typically the top will at first wobble until friction and torque between the tip and the underlying surface force it to spin with the axis steady and upright. Contrary to what is sometimes assumed, longstanding scientific studies (and easy experimentations reproducible by anyone) show that reducing the friction increases the time needed to reach this stable state (unless the top is so unbalanced that it falls over before reaching it). [7] After spinning upright (in the so-called "sleep" position) for an extended period, the angular momentum will gradually lessen (mainly due to friction), leading to ever increasing precession, finally causing the top to topple and roll some distance on its side. In the "sleep" period, and only in it, provided it is ever reached, less friction means longer "sleep" time (whence the common error that less friction implies longer global spinning time).

The total spinning time of a top is generally increased by increasing its moment of inertia and lowering its center of gravity. [7] These variables however are constrained by the need to prevent the body from touching the ground.

Asymmetric tops of virtually any shape can also be created and designed to balance. [8]

Competitions

There are many official competitions of top spinning, such as the U. S. National Championships in Chico, California and in the World Championships in Orlando, Florida.[ citation needed ]

The Jean Shepherd story "Scut Farkas and the Murderous Mariah" revolves around top-spinning in the fictional Depression-era American city of Hohman, Indiana. The bully and the named top in the title are challenged by Shepherd's ongoing protagonist Ralph and a so-called "gypsy top" of similar design to Mariah named Wolf. [9]

The Top is a short story by bohemian writer Franz Kafka.

The top is a focal element and metaphysical symbol in the movie Inception , directed by Christopher Nolan and starring Leonardo DiCaprio. In the final shot, the camera moves over the spinning top just before it appears to be wobbling.

See also

Related Research Articles

Angular momentum Physical quantity

In physics, angular momentum is the rotational equivalent of linear momentum. It is an important quantity in physics because it is a conserved quantity—the total angular momentum of a closed system remains constant.

Nutation

Nutation is a rocking, swaying, or nodding motion in the axis of rotation of a largely axially symmetric object, such as a gyroscope, planet, or bullet in flight, or as an intended behaviour of a mechanism. In an appropriate reference frame it can be defined as a change in the second Euler angle. If it is not caused by forces external to the body, it is called free nutation or Euler nutation. A pure nutation is a movement of a rotational axis such that the first Euler angle is constant. In spacecraft dynamics, precession is sometimes referred to as nutation.

Precession Periodic change in the direction of a rotation axis

Precession is a change in the orientation of the rotational axis of a rotating body. In an appropriate reference frame it can be defined as a change in the first Euler angle, whereas the third Euler angle defines the rotation itself. In other words, if the axis of rotation of a body is itself rotating about a second axis, that body is said to be precessing about the second axis. A motion in which the second Euler angle changes is called nutation. In physics, there are two types of precession: torque-free and torque-induced.

Rotation Movement of an object around an axis

A rotation is a circular movement of an object around a center of rotation. The geometric plane along which the rotation occurs is called the rotation plane, and the imaginary line extending from the center and perpendicular to the rotation plane is called the rotation axis. A three-dimensional object can always be rotated about an infinite number of rotation axes.

Gyroscope Device for measuring or maintaining orientation and direction

A gyroscope is a device used for measuring or maintaining orientation and angular velocity. It is a spinning wheel or disc in which the axis of rotation is free to assume any orientation by itself. When rotating, the orientation of this axis is unaffected by tilting or rotation of the mounting, according to the conservation of angular momentum.

Flywheel Mechanical device for storing rotational energy

A flywheel is a mechanical device specifically designed to use the conservation of angular momentum so as to efficiently store rotational energy; a form of kinetic energy proportional to the product of its moment of inertia and the square of its rotational speed. In particular, if we assume the flywheel's moment of inertia to be constant then the stored (rotational) energy is directly associated with the square of its rotational speed.

Yo-yo Toy

A yo-yo is a toy consisting of an axle connected to two disks, and a string looped around the axle, similar to a spool. It is played by holding the free end of the string known as the handle, allowing gravity to spin the yo-yo and unwind the string. The player then allows the yo-yo to wind itself back to the player's hand, exploiting its spin. This is often called "yo-yoing".

Diabolo Juggling prop consisting of an axle and two cups or discs

The diabolo is a juggling or circus prop consisting of an axle and two cups or discs derived from the Chinese yo-yo. This object is spun using a string attached to two hand sticks. A large variety of tricks are possible with the diabolo, including tosses, and various types of interaction with the sticks, string, and various parts of the user's body. Multiple diabolos can be spun on a single string.

Whirligig Object that spins or whirls

A whirligig is an object that spins or whirls, or has at least one part that spins or whirls. A whirligig can also be a pinwheel, buzzer, comic weather-vane, gee-haw, spinner, whirlygig, whirlijig, whirlyjig, whirlybird, or simply a whirly. Whirligigs are most commonly powered by the wind but can be hand, friction, or motor powered. They can be used as a kinetic garden ornament. They can also be designed to transmit sound and vibration into the ground to repel burrowing rodents in yards.

Astrojax

Astrojax, invented in 1986 by Larry Shaw, is a toy consisting of three balls on a string. One ball is fixed at each end of the string, and the center ball is free to slide along the string between the two end balls. Inside each ball is a metal weight. The metal weight lowers the moment of inertia of the center ball so it can rotate rapidly in response to torques applied by the string. This prevents the string from snagging or tangling around the center ball.

Rattleback

A rattleback is a semi-ellipsoidal top which will rotate on its axis in a preferred direction. If spun in the opposite direction, it becomes unstable, "rattles" to a stop and reverses its spin to the preferred direction.

Rotation around a fixed axis Type of motion

Rotation around a fixed axis is a special case of rotational motion. The fixed-axis hypothesis excludes the possibility of an axis changing its orientation and cannot describe such phenomena as wobbling or precession. According to Euler's rotation theorem, simultaneous rotation along a number of stationary axes at the same time is impossible; if two rotations are forced at the same time, a new axis of rotation will appear.

Trompo Spinning object

A Trompo is a top which is spun by winding a length of string around the body, and launching it so that lands spinning on its point. If the string is attached to a stick the rotation can be maintained by whipping the side of the body. The string may also be wound around the point while the trompo is spinning in order to control its position or even lift the spinning top to another surface.

In classical mechanics, Poinsot's construction is a geometrical method for visualizing the torque-free motion of a rotating rigid body, that is, the motion of a rigid body on which no external forces are acting. This motion has four constants: the kinetic energy of the body and the three components of the angular momentum, expressed with respect to an inertial laboratory frame. The angular velocity vector of the rigid rotor is not constant, but satisfies Euler's equations. Without explicitly solving these equations, Louis Poinsot was able to visualize the motion of the endpoint of the angular velocity vector. To this end he used the conservation of kinetic energy and angular momentum as constraints on the motion of the angular velocity vector . If the rigid rotor is symmetric, the vector describes a cone. This is the torque-free precession of the rotation axis of the rotor.

The details of a spinning body may impose restrictions on the motion of its angular velocity vector, ω. The curve produced by the angular velocity vector on the inertia ellipsoid, is known as the polhode, coined from Greek meaning "path of the pole". The surface created by the angular velocity vector is termed the body cone.

Beyblade Spinning top toy

Beyblade is a line of spinning top toys originally developed by Takara, first released in Japan in July 1999, along with its debut series. Following Takara's merger with Tomy in 2006, Beyblades are now developed by Takara Tomy. Various toy companies around the world have licensed Beyblade toys for their own regions, including Hasbro in Western countries, Sonokong in South Korea, and Takara Tomy for Eastern countries.

Twirling

Twirling is a form of object manipulation where an object is twirled by one or two hands, the fingers or by other parts of the body. Twirling practice manipulates the object in circular or near circular patterns. It can also be done indirectly by the use of another object or objects as in the case of devil stick manipulation where handsticks are used. Twirling is performed as a hobby, sport, exercise or performance.

Tippe top

A tippe top is a kind of top that when spun, will spontaneously invert itself to spin on its narrow stem.

Gyroscopic exercise tool

A gyroscopic exercise tool is a device used to exercise the wrist as part of physical therapy or in order to build palm, forearm and finger strength. It can also be used as a unique demonstration of some aspects of rotational dynamics. The device consists of a tennis ball-sized plastic or metal shell around a free-spinning mass, which is started with a short rip string. Once the gyroscope inside is going fast enough, a person holding the device can accelerate the spinning mass to high revolution rates by moving the wrist in a circular motion.

References

  1. D. W. Gould (1973). The Top. NY: Clarkson Potter. ISBN   0-517-50416-2.[ page needed ]
  2. Gould (1973), p.20-4.
  3. Peter Michael Harman (1998). The Natural Philosophy of James Clerk Maxwell. Cambridge University Press. ISBN   0-521-00585-X. Archived from the original on 2017-12-27.
  4. James Clerk Maxwell (2003). The Scientific Papers of James Clerk Maxwell. Dover Publications. ISBN   0-486-49560-4. Archived from the original on 2017-12-27.
  5. Gould (1973), p.32.
  6. National Recreation Association (1965). Recreation. p. 92. Archived from the original on 2013-11-13.
  7. 1 2 H. Crabtree (1909). An Elementary Treatment of the Theory of Spinning Tops and Gyroscopic Motion. London: Longman, Green and C.
  8. Bächer, Moritz; Whiting, Emily; Bickel, Bernd; Sorkine-Hornung, Olga (August 10–14, 2014). "Spin-It: Optimizing Moment of Inertia for Spinnable Objects" (PDF). ACM Conference on Computer Graphics & Interactive Techniques (SIGGRAPH) 2014. Archived from the original (PDF) on 10 August 2014. Retrieved 15 August 2014.
  9. Shepherd, Jean. "Scut Farkas and the Murderous Mariah", Wanda Hickey's Night of Golden Memories and Other Disasters (New York: Doubleday Dolphin Books), 1976 ISBN   0-385-11632-2

Further reading