Gyroscopes in Physics - Report Example

Introduction. A gyroscope is a rotating body, which has gyroscopic inertia or rigidity in space, and the property of precession or the tilting of the axis at right angles to any force trying to alter its plane of rotation. These properties are intrinsic to all rotating bodies, including the earth. Spherical, wheel-shaped or disk-shaped bodies that are mounted to rotate in any direction and used to demonstrate these properties or to indicate movements in space are called gyroscopes. A gyrostat is a gyroscope, which moves only on its axis of rotation and almost all practical applications use gyrostats. Gyroscopic Inertia. The precession of a gyroscope results from Newtons first law of motion , which states that if a body is at rest or is moving with constant velocity, then if the vector sum of the forces acting on it is zero, the body will remain at rest or keep moving with constant velocity. The spinning wheel of a gyroscope tends to continue to rotate in the same plane about the same axis. An example of this is a spinning top, which has freedom about two axes in addition to the spinning axis. Another example is a rifle bullet, which due to the spin traverses a straighter line of flight due to gyroscopic inertia. The best demonstration of this effect is a model gyroscope consisting of a flywheel supported in rings in such a way that the axle of the flywheel can assume any angle in space. When the flywheel is spinning, the model can be moved about, tipped, or turned without the flywheel deviating from its original plane of rotation as long as it spins with sufficient velocity to overcome the friction with its supporting bearings. (Lawrence, 1998: 87-94). Precession. Precession is the regular spinning motion of a body, in which the axis of rotation describes a cone. If a force is applied to a gyroscope to change the direction of the axis of rotation, the axis will move in a direction at right angles to the direction of the applied force due to the resultant force produced by the angular momentum of the rotating body and the applied force. A simple example is the rolling hoop, to turn the hoop; guiding pressure has to be applied not to the front or to the rear of the hoop, but against the top and this pressure, although applied about a horizontal axis, does not cause the hoop to fall over, but causes it to precess about the vertical axis at right angles to the applied pressure, with the result that it turns and proceeds in a new direction. (Serway and Jewett, 2005: 319-332). Evolution. The ancient Greek, Chinese and Roman societies built the spinning top, a toy which balanced upright while rotating rapidly. The Maori in New Zealand used humming tops, with specially-crafted holes, in mourning ceremonies. In 14th century England, some villages had a large top constructed for a warming-up exercise in cold weather. Tops were even used in place of dice, like the die in the contemporary fantasy game Dungeons &Dragons. The first modern gyroscope was designed in the early 1800s by Johann Gottlieb Friedrich von Bohnenberger, a professor at the University of Tuebingen, Germany. It was made with a heavy ball instead of a wheel, but since it had no scientific application, it was forgotten. The French scientist Leon Foucault in an attempt to observe the rotation of the used a spinning top as a pendulum. He placed a wheel, rotating at high-speed, in a supporting ring such that the axis of the spinning wheel could move independently of the ring. The supporting ring moved over the course of a day, as it was connected to the surface of the rotating Earth. The axis of the wheel remained pointed in its original direction, confirming that the Earth was rotating in a twenty-four hour period. Foucault named his spinning wheel a "gyroscope," from the Greek words "gyros" (revolution) and "skopein" (to see); he had seen the revolution of the Earth with his gyroscope. Fifty years later in 1898 the Austrian Ludwig Obry patented a torpedo steering mechanism based on gyroscopic inertia. In the early 20th Century, Elmer A.Sperry developed the first automatic pilot for airplanes using a gyroscope, and installed the first gyrostabilizer to reduce roll on ships. While gyroscopes were not initially very successful at navigating ocean travel, navigation is their predominant use today. They can be found in ships, missiles, airplanes, the Space Shuttle and satellites. (Bunch, 2004: 352-380). Gyroscope Physics. A gyroscope has three axes. First, a spin axis, which defines the gyroscope strength or moment and two other axes called the primary axis and the secondary axis. These three axes are orthogonal to each other. The spin axis rotates around the vertical line. The primary axis rotates the whole gyroscope in the plane of the page, and the secondary axis rotates the gyroscope up-and-over into the page. The spin axis is the source of the gyroscopic effect. The primary axis is the input or driving axis and the secondary the output. If the gyroscope is spun on its spin axis and a torque is applied to the primary axis the secondary axis will precess. The primary axis appears infinitely stiff to the applied torque and does not give under it. This is the generally recognized characteristic of gyroscopic behaviour. It is important not to confuse the concepts of angular momentum and gyroscopic moment. When a mass ‘m’ moves in a straight line at velocity ‘v’ it exhibits linear momentum (mv). It is trivial to predict that if it is constrained to travel in a radius ‘r’ it will produce an angular momentum (mvr). However with the angular momentum an effect that could not have been predicted turns up - gyroscopic behaviour. The fact that these two effects occur together and in simple proportion to each other does not mean that this is always the case - gyroscopic behaviour occurs without angular momentum in electron behaviour, even though the terms ‘spin’ and ‘spin angular momentum’ are still used for historical reasons and even though there is no direct evidence that the electron’s mass or charge spins on its own axis. It may simply be that rotating an object exposes the gyroscopic moments of the elementary particles that make it up, possibly through the asymmetric relativistic effects created by the centripetal acceleration; this is a conjecture requiring major experimental work. Angular momentum has the form “kilogram-meters2 per second”. Gyroscopic moment has the form “Newton-meters per Hertz”, or torque required to produce a precession rate of one Hertz. Both have the dimensions ‘ML2T-1’, which implies that they are related by a simple scalar number. Basic Gyroscope Equations. Let G denote the strength of a gyroscopic effect or the gyroscopic moment, its units are “Newton-meters/Hertz”. A higher moment requires more torque to precess at the same frequency, or for the same torque precesses at a lower rate. Where a gyroscope receives torque on the primary axis and precession on the secondary, no work is being done. The torque ‘TP’ on the primary axis has no precession associated with it, while the precession rate ‘vS’ on the secondary axis is given by, vS = TP / G. and has no torque associated with it. Since the rate of doing work on each axis is the torque times the precession on that axis, it follows that no energy is expended. Simultaneous torque on both the axes results in simultaneous precession. In this case each axis will have both torque (creating precession on the other axis) and precession (created by torque on the other axis). In this case the rate of doing work ‘PP’ on the primary axis is given by, PP = TP.vP / G, and on the secondary axis by PS = TS.vS / G, by the principle of conservation of energy, PP = - PS, i.e. the work done on one axis must appear on the other. Let it be assumed that a forcing torque is applied to the primary axis and that the primary axis presents no stiffness against the forcing torque. Then the secondary axis precesses at an infinite frequency, but for a limiting mechanism that comes into play; just as torque creates precession, so precession creates torque. So as the secondary axis precesses it creates a reverse torque TPF on the primary axis given by, TPF =  -vS.G The precession rate always runs at that point where TPF is exactly equal and opposite to TP. At this point, TPF = -vS.G = - ( TP / G ).G = - TP. The reverse torque generated by the precession exactly opposes the applied torque so that the net torque is zero. If it was more the work would be done by the gyroscope. If it was less the primary axis would give way under the applied torque and work would be done with no outlet for it. Both these conditions violate conservation of energy principles. Hence, the gyroscope precesses on the secondary axis to exactly oppose the applied torque on the primary axis. This leads to an aspect of gyroscopic behaviour that is important in the behaviour of electrons, if the secondary axis is locked against rotation and the primary axis is driven, no opposing torque will appear on the primary axis, it is free to rotate without hindrance. No work is transferred through the gyroscope; there is motion without torque on the primary axis. The secondary axis has no motion but instead experiences a torque TSF, given by TSF = vP.G This is identical to basic gyroscope operation, but viewed from the other side. Instead of saying that torque on the primary axis leads to precession on the secondary we say that precession on the secondary axis leads to torque on the primary axis (Goodman and Warner, 2001: 448-496). List of References. Bunch, Bryan, (16 Apr 2004) The History of Science and Technology: A Browsers Guide to the Great Discoveries, Inventions,....Houghton Mifflin Books. ISBN: 0618221239. Goodman, E Lawrence and Warner, William H,(8 Oct 2001) Dynamics. Courier Dover Publications. ISBN: 048642006X. Lawrence, Anthony, (1 Sep 1998) Modern Inertial Technology. Springer. ISBN: 0387985077. Serway, Raymond A and Jewett, John W,(1 Feb 2005) Principles Of Physics: A Calculus-Based Text (with Physics now).Thomson Brooks/Cole. ISBN: 053449143X. Read More

The French scientist Leon Foucault in an attempt to observe the rotation of the used a spinning top as a pendulum. He placed a wheel, rotating at high-speed, in a supporting ring such that the axis of the spinning wheel could move independently of the ring. The supporting ring moved over the course of a day, as it was connected to the surface of the rotating Earth. The axis of the wheel remained pointed in its original direction, confirming that the Earth was rotating in a twenty-four hour period.

Foucault named his spinning wheel a "gyroscope," from the Greek words "gyros" (revolution) and "skopein" (to see); he had seen the revolution of the Earth with his gyroscope. Fifty years later in 1898 the Austrian Ludwig Obry patented a torpedo steering mechanism based on gyroscopic inertia. In the early 20th Century, Elmer A.Sperry developed the first automatic pilot for airplanes using a gyroscope, and installed the first gyrostabilizer to reduce roll on ships.

While gyroscopes were not initially very successful at navigating ocean travel, navigation is their predominant use today. They can be found in ships, missiles, airplanes, the Space Shuttle and satellites. (Bunch, 2004: 352-380). Gyroscope Physics. A gyroscope has three axes. First, a spin axis, which defines the gyroscope strength or moment and two other axes called the primary axis and the secondary axis. These three axes are orthogonal to each other. The spin axis rotates around the vertical line.

The primary axis rotates the whole gyroscope in the plane of the page, and the secondary axis rotates the gyroscope up-and-over into the page. The spin axis is the source of the gyroscopic effect. The primary axis is the input or driving axis and the secondary the output. If the gyroscope is spun on its spin axis and a torque is applied to the primary axis the secondary axis will precess. The primary axis appears infinitely stiff to the applied torque and does not give under it. This is the generally recognized characteristic of gyroscopic behaviour.

It is important not to confuse the concepts of angular momentum and gyroscopic moment. When a mass ‘m’ moves in a straight line at velocity ‘v’ it exhibits linear momentum (mv). It is trivial to predict that if it is constrained to travel in a radius ‘r’ it will produce an angular momentum (mvr). However with the angular momentum an effect that could not have been predicted turns up - gyroscopic behaviour. The fact that these two effects occur together and in simple proportion to each other does not mean that this is always the case - gyroscopic behaviour occurs without angular momentum in electron behaviour, even though the terms ‘spin’ and ‘spin angular momentum’ are still used for historical reasons and even though there is no direct evidence that the electron’s mass or charge spins on its own axis.

It may simply be that rotating an object exposes the gyroscopic moments of the elementary particles that make it up, possibly through the asymmetric relativistic effects created by the centripetal acceleration; this is a conjecture requiring major experimental work. Angular momentum has the form “kilogram-meters2 per second”. Gyroscopic moment has the form “Newton-meters per Hertz”, or torque required to produce a precession rate of one Hertz. Both have the dimensions ‘ML2T-1’, which implies that they are related by a simple scalar number.

Basic Gyroscope Equations. Let G denote the strength of a gyroscopic effect or the gyroscopic moment, its units are “Newton-meters/Hertz”. A higher moment requires more torque to precess at the same frequency, or for the same torque precesses at a lower rate. Where a gyroscope receives torque on the primary axis and precession on the secondary, no work is being done. The torque ‘TP’ on the primary axis has no precession associated with it, while the precession rate ‘vS’ on the secondary axis is given by, vS = TP / G.

and has no torque associated with it.

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