Precession
From Wikipedia, the free encyclopedia
Precession refers to a change in the direction of the axis of a rotating object. In physics, there are two types of precession, torque-free and torque-induced, the latter being discussed here in more detail. In certain contexts, "precession" may refer to the precession that the Earth experiences, the effects of this type of precession on astronomical observation, or to the precession of orbital objects.
Contents |
[edit] Torque-free precession
Only moving objects can be in torque-free precession. For example, when a plate is thrown, the plate may have some rotation around an axis that is not its axis of symmetry. When the object is not perfectly solid, internal vortices will tend to damp torque-free precession.
[edit] Torque-induced precession
Torque-induced precession (gyroscopic precession) is the phenomenon by which the axis of a spinning object (e.g. a part of a gyroscope) "wobbles" when a torque is applied to it. The phenomenon is commonly seen in a spinning toy top, but all rotating objects can undergo precession. If the speed of the rotation and the magnitude of the torque are constant the axis will describe a cone, its movement at any instant being at right angles to the direction of the torque. In the case of a toy top, if the axis is not perfectly vertical the torque is applied by the force of gravity trying to tip it over. A rolling wheel will tend to remain upright due to precession. When the wheel tilts to one side, the particles at the top are pushed to one side and the particles at the bottom are pushed the other way. However, since the wheel is rotating, these particles eventually switch places and cancel one another out. Precession or gyroscopic considerations have an effect on bicycle performance at high speed. Precession is also the mechanism behind gyrocompasses.
This concept is easier to understand by examining the effects of inertia, which is often stated by the phrase "A body in motion tends to stay in motion." In this case the "motion" of a rotating body is in its rotation. If an external force pushes upon the rotating body, the body will resist the force by pushing back against it, but the reaction is delayed.
Gyroscopic precession also plays a large role in the flight controls on helicopters. Since the driving force behind helicopters is the rotor disk (which rotates), gyroscopic precession comes into play. If the rotor disk is to be tilted forward (to gain forward velocity), its counter-clockwise movement requires that the downward net force on the blade be applied roughly 90 degrees (depending on blade configuration) before, or when the blade is to the right of the pilot. To ensure the pilot's inputs are correct, the aircraft has corrective linkages which tilt the swashplate to the right when the pilots push the "cyclic stick" forward, or to the left when the stick is pulled to the back.
A disadvantage of precession is that it can cause fastenings under large torque loads to unscrew themselves. Bicycle pedals are left-threaded on the left-hand crank so that precession tightens the pedal rather than causing it to come loose. Before the advent of taper lug nuts which are immune to precession, some automobiles also used left-threaded nuts for the left side road wheels.
[edit] The physics of precession
Precession is the resultant of the angular velocity of rotation and the angular velocity produced by the torque. It is an angular velocity about a line which makes an angle with the permanent rotation axis, and this angle lies in a plane at right angles to the plane of the couple producing the torque. The permanent axis must turn towards this line, since the body cannot continue to rotate about any line which is not a principal axis of maximum moment of inertia; that is, the permanent axis turns in a direction at right angles to that in which the torque might be expected to turn it. If the rotating body is symmetrical and its motion unconstrained, and if the torque on the spin axis is at right angles to that axis, the axis of precession will be perpendicular to both the spin axis and torque axis. Under these circumstances the period of precession is given by:
In which Is is the moment of inertia, Ts is the period of spin about the spin axis, and Q is the torque. In general the problem is more complicated than this, however.
For a layman’s explanation of Precession: we will have to imagine the wheel of a gyroscope as a group of particles that are being forced to move in circle. Remember the particles want to move in a straight line. In order for the particles to move in a curved line there must be a force. This force is provided by the structure of the wheel holding the particles within the wheel.
Now let’s see what happens to our accelerating particles when a torque is applied to the spinning wheel. Assume the axis of rotation created by the torque is through the center of the wheel at 90 degrees to the primary rotation of the wheel. Let’s look at a particle that is on this axis of rotation. Since the particle is on the axis of rotation there is no direct motion applied to the particle at the instant of the applied torque. But let’s look at what will need to happen at the next moment in time. The particle is now going to be forced to curve again. This time in the direction of the curve so as to accommodate the tilt of the wheel. Now we have a particle that is already moving and it wants to keep moving in a straight line. So the particle will exert a force on the wheel. If you look at a particle on the other side of the wheel you will see that the force of the second particle is in the opposite direction of the first particle. That pair of unmatched forces is what causes the precession torque that is 90 degrees to the applied torque.
[edit] Precession of the equinoxes
The Earth goes through one complete precession cycle in a period of approximately 25,800 years, during which the positions of stars as measured in the equatorial coordinate system will slowly change; the change is actually due to the change of the coordinates. Over this cycle the Earth's north axial pole moves from where it is now, within 1° of Polaris, in a circle around the ecliptic pole, with an angular radius of about 23.5 degrees (exactly 23 degrees 27 arcminutes [1]). The shift is 1 degree in 180 years, where the angle is taken from the observer, not from the center of the circle.
The precession of the equinoxes was discovered in antiquity by the Greek astronomer Hipparchus, and was later explained by Newtonian physics. The Earth has a nonspherical shape, being oblate spheroid, bulging outward at the equator. The gravitational tidal forces of the Moon and Sun apply torque as they attempt to pull the equatorial bulge into the plane of the ecliptic. The portion of the precession due to the combined action of the Sun and the Moon is called lunisolar precession.
[edit] Precession of planetary orbits
The revolution of a planet in its orbit around the Sun is also a form of rotary motion. (In this case, the combined system of Earth and Sun is rotating.) So the axis of a planet's orbital plane will also precess over time.
The major axis of each planet's elliptical orbit also precesses within its orbital plane, in response to perturbations in the form of the changing gravitational forces exerted by other planets. This is called perihelion precession or apsidal precession (see apsis). Discrepancies between the observed perihelion precession rate of the planet Mercury and that predicted by classical mechanics were prominent among the forms of experimental evidence leading to the acceptance of Einstein's Theory of Relativity, which predicted the anomalies accurately.[2]
It is generally understood that the gravitational pulls of the Sun and the Moon cause the precession of the Earth's orbit which affect climate with cycles of 23,000 and 19,000 years. These periodic changes of the orbital parameters, as well as that of the inclination of the Earth's axis on its orbit, are an important part of the astronomical theory of ice ages. For precession of the lunar orbit see lunar precession.
An analogous phenomenon to apsidal precession is nodal precession (see orbital node), which affects the orientation of the orbital plane.
Precession is also an important consideration in the dynamics of atoms and molecules.
[edit] See also
- Discovery of precession
- Geometric precession
- Larmor precession
- Polar motion
- Thomas precession
- Astrological age
[edit] Notes
- ^ Cook, David R. (1999). Tilt of Earth's Axis. Environmental Earth Science Archive, Ask A Scientist. United States Department of Energy. Retrieved on 2006-05-24.
- ^ Max Born (1924), Einstein's Theory of Relativity (The 1962 Dover edition, page 348 lists a table documenting the observed and calculated values for the precession of the perihelion of Mercury, Venus, and Earth.)
[edit] References
- "Moon and Spica", StarDate July 14, 2005, University of Texas McDonald Observatory, [1]
