Precession

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Precession of a gyroscope
Precession of a gyroscope

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.

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[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 in 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 tending 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.

Precession causes a force applied to a spinning wheel to be felt 90° from the point of application in the direction of rotation.
Precession causes a force applied to a spinning wheel to be felt 90° from the point of application in the direction of rotation.

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.

[edit] Fretting induced precession

Fretting can cause unscrewing "from precession, in which a round object rolling in a circular ring in one direction will itself turn in the opposite direction." "In machinery, fretting is the micro-motion of tightly fitting parts that superficially appear immobile with respect to each other."[1]

"For a pedal, a rotating load arises from downward pedaling force on a spindle rotating with its crank making the predominantly downward force effectively rotate about the pedal spindle. What may be less evident is that even tightly fitting parts have relative clearance due to their elasticity, metals not being rigid materials as is evident from steel springs. Under load, micro deformations, enough to cause motion, occur in such joints. This can be seen from wear marks where pedal spindles seat on crank faces."[2]

Fretting-induced precession is completely unrelated to torque-free and torque-induced precession as defined above. It is a purely mechanical process which does not depend on inertia and is not inversely proportional to spin rate.

Fretting can cause fastenings under large torque loads to unscrew themselves. Bicycle pedals are left-threaded on the left-hand crank arm so that precession tightens the pedal rather than loosening it. Automobiles have also used left-threaded lug nuts on left-side wheels, but now commonly use tapered lug nuts, which do not fret.

[edit] The physics of precession

Precession is the result 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 angular velocity of precession is given by:

\boldsymbol\omega_p = \frac{Q}{I_s\boldsymbol\omega_s}

In which Is is the moment of inertia, \boldsymbol\omega_s is the angular velocity of spin about the spin axis, and Q is the torque. Using \boldsymbol\omega = \frac{2\pi}{T}, we find that the period of precession is given by:

T_p = \frac{4\pi^2I_s}{QT_s}

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.

An informal explanation of Precession: In a classic beginning physics demonstration, the instructor stands on a swiveling platform and holds a spinning bicycle wheel at arm's length. The wheel is vertical and the instructor is standing still. The instructor then tilts the wheel toward horizontal. This causes the instructor to start spinning slowly on the platform. Bringing the wheel back to vertical and tilting it the other way makes the instructor spin the other way. Why?

Imagine the wheel as a collection of small particles. Particles want to move in a straight line. In order for them to move in a circle there must be a force accelerating the particles toward the center of the circle (acceleration is a change in speed or direction or both — in this case just direction). This force is ultimately provided by bonds between the atoms in the wheel and spokes.

What happens when the instructor turns the spinning wheel from vertical to horizontal? Consider a particle somewhere on the wheel. If the wheel weren't being tilted, it would be accelerated around the circle as always. But since the wheel is tilting, it now has to follow a new path. A change in path is an acceleration, which in turn requires force (from the instructor's hands, transmitted through the spokes to the rim). Now consider the particle opposite the first particle on the wheel. It also has to change path, but in the opposite direction. Since the forces on opposite sides are in opposite directions, the result is torque. Each pair of opposite particles on the wheel contributes to the torque that causes the instructor to turn on the platform.

Tilting the wheel the other direction produces torque in the opposite direction, slowing the instructor's spin and eventually reversing it.

[edit] Precession of the equinoxes

Main article: Precession of the equinoxes
Precessional movement.
Precessional movement.

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 [3]). 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

Precession of the perihelion (very exaggerated)
Precession of the perihelion (very exaggerated)

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.[4]

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



[edit] References

  1. ^ Fretting damage in Bicycle Mechanics. Retrieved on 2006-12-26.
  2. ^ Brandt, Jobst (2004/5). Left Hand Threads. Retrieved on 2006-12-26.
  3. ^ 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.
  4. ^ 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.)
  • "Moon and Spica", StarDate July 14, 2005, University of Texas McDonald Observatory, [1]
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