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A gyroscope is a ( rigid ) body which rotates about an axis. He may otherwise move freely, but can also be held on a shaft end or both, more or less. Centrifugal need not necessarily be rotationally symmetrical in physics.

As a gyro or gyro ( griechisch. ) but also instruments are referred to carry out similar tasks, such as a gyroscope, even if they do not contain a rotating gyroscope. Examples are laser gyros, fiber optic gyros or vibration gyro.

Roundabout as children's toys

Centrifugal serve as children's toys, which is rotated on a base about a vertical axis, and then held for a while about the axial direction maintains, the gyro moves around on the surface.

The gyroscope is one of the oldest toys, which can be found at archaeological sites. Except as a toy gyroscope has historically been used for gambling and for divination. In technology, gyroscopes are used for example for the stabilization and navigation, since the direction of the angular momentum remains the same if no force acts on it. The reason for this is the conservation of angular momentum. Determines the rotation axis in line with the direction of the angular momentum, also does not change this.

Physical viewing

In the physical sense, a rotating rigid body is a roundabout. Also considered are mathematically rotating solid -state gyro.

The behavior of the toy top is based on the gyroscopic effect. Normally, the centrifugal wobble first to the interaction between the tip and the bottom surface forces the rotors in an upright position. After a prolonged upright rotating phase of the angular momentum and therefore the gyroscopic effect will become less. This leads to a precession is increasing, eventually dragging ends in a strong tendency to tilt.

Equations of motion

The motion of the top is caused by the angular momentum conservation. The angular momentum is the product of inertia tensor, and the rotary speed of the gyro. As the mass indicates the moment of inertia, as it is " difficult " to change the rotational motion. If we calculate the change of the angular momentum L by its derivative with respect to time yields:

That is, the change of the angular momentum is proportional to the change in angular velocity and equal to the torque

Looking at the individual components of the vectors, the result is a system of differential equations, which are named after their discoverer, Leonhard Euler. See also the main article Euler equations. The letter I in the formula for the inertia tensor, a " collection " of the moments of inertia for rotation about different axes in a matrix. There are two axes with respect to which the inertia of the body is at a maximum or minimum, rotation about these axes is stable. These axes are always perpendicular to each other and, together with a third, again perpendicular to both axis the principal axes of inertia of the body. In a plane spanned by the principal axes coordinate system of the inertia tensor is diagonal, which greatly simplifies calculations. Belonging to the principal axes of inertia moments of inertia are thus the eigenvalues ​​of the inertia tensor, they are called principal moments of inertia.

Classification and Characteristics

• For a symmetric top, at least two principal moments of inertia are equal. This group includes the rotationally symmetric toy top or cuboid with two equal sides. One of its principal axes coincides with the axis of figure together, perpendicular to it, by its focus, it has infinitely many identical equatorial principal axes. The ellipsoid of inertia of a symmetric top is always rotationally symmetric. In three different principal moments of inertia is called an asymmetric top.
• For a spherical gyroscope all three principal moments of inertia are equal. Examples are cubes and spheres. A sphere has an infinite number of identical principal axes.
• A gyroscope is a force-free if no external torques act on him, ie all external forces outside the center of gravity must cancel each other. To this end, the support point for the gyro has for example just below the center of gravity of the gyroscope, as gimbal (focus in the center of the gimbal ), or as a small shear centrifugal (support directly in the center of gravity of a hollowed-out bottom gyro body ). The equations of motion for a force-free symmetric top are easier to solve than for a heavy top. Its movement is generally made of the actual rotation and nutation. In the nutation have the angular momentum and the instantaneous axis of rotation different directions. This occurs when the moment of inertia depends on the direction ( the moments of inertia are not all the same size ) and not done the rotation around the axis of a principal moment of inertia. The gyroscope is not symmetrical, it can lead to more complex movements.
• The opposite is the heavy gyro: If a toy top, for example, inclined, gravity tries to upset him. Since the resulting torque is perpendicular to the angular momentum, the angular momentum changes only its direction. The gyro rotates around an axis that passes perpendicularly through its contact point to the top. This rotation is called precession. The equations of motion are solved here only approximately (especially for fast spinning top ).

Examples of centrifugal

The toys are available in numerous models and versions:

• Brummkreisel
• Drawing centrifugal
• Game centrifugal
• Peitschenkreisel
• Pfeifkreisel
• Duel centrifugal Beyblade
• Beigoma

Application

Technical applications are:

• Gyroscope ( measurement axis) and gyro (measurement of the rotational speed )
• Roundabout as energy storage (see also rotary mass storage ).
• Inertia wheels for attitude control of missiles
• The Levitron is a magnetic gyro Direction hovering over an oppositely poled, annular magnetic field in the air. Its centrifugal motion prevents it tilts and is attracted by the magnet ring. - Video ( Ogg; 1.13 Mbps)
• The gyro compass is directed - by the rotation of the earth - in the direction of the North Pole.

Beginning of the 20th century, centrifugal - used for the study of human perception of color - for example, the Musilsche color top.

Popular culture

In the movie Inception in the year 2010, the protagonist Cobb uses a gyroscope as " Totem".