During the course of the Skylab mission, there were many occasions on which the crew demonstrated important aspects of classical mechanics that are difficult to produce on Earth. Historically, mechanics was the earliest branch of physics developed into an exact science. Archimedes, in the 3d century B.C. said, "Give me a lever long enough, and a place to stand, and I will move the Earth." It remained for Isaac Newton, 17 centuries later, to first give a complete formulation of the laws of mechanics as follows:
(1) Every body continues in its state of rest or of uniform motion in a straight line unless it is compelled to change that state by forces impressed upon it.
(2) Rate of change of momentum is proportional to the impressed force and is in the direction in which the force acts.
(3) To every action there is always an equal and opposite reaction.
Conservation of Momentum
Figure skaters often demonstrate Newton's second law on ice. With arms outstretched, they start a slow spin and then quickly bring their feet together and told their arms across the chest. These movements decrease the moment of inertia about the spin axis, causing a rapid increase in angular velocity to maintain constant angular momentum.
In the weightless environment of Skylab, the astronauts performed similar demonstrations. Pushing off from the wall of the 21-foot-diameter upper compartment of the orbital workshop, they flipped and tumbled at varying rates that they controlled by extending or retracting their arms and legs. They also demonstrated perfect military facing maneuvers starting from a motionless, free-floating condition. By spreading the legs fore and aft, then rotating them to the left, the body follows, coming to rest 90 degrees from the original position. Similarly, a free-floating flip was performed by swinging the arms in a circle. When the arms were stopped, the flip stopped.
Spinning a partially filled beverage container showed yet another example of the principle of the conservation of momentum. However, an additional concept was introduced: the conservation of energy. Spinning a plastic bottle about its major axis, the axis of minimum moment of inertia, might be expected to be a stable mode of rotation. In fact, the designers of the Explorer I artificial satellite, launched in 1958, stabilized it by spinning it about its major axis. Before long, Explorer I was tumbling in its orbit. This same effect was demonstrated with the drink container.
Rotation of the partially filled, flexible container resulted in converting some of the rotational energy into heat due to turbulence. The total energy of the system had to remain constant, but the conversion of some rotational energy to heat caused the spin rate or angular velocity to decrease. Since angular momentum, which is the product of angular velocity and moment of inertia, must....
 ....remain constant, the moment of inertia had to increase. In order for this to occur. the bottle rotated about a new axis of greater inertia. The bottle, therefore, started to wobble and ultimately to tumble or rotate about a transverse axis at a slower rate. Once tumbling about the axis of maximum moment of inertia was established. the fluid distributed itself uniformly at the ends of the beverage container. No more turbulence was experienced. and the tumbling became the stable mode of rotation. In the case of the Explorer I satellite, four long, flexible antennas absorbed enough energy to induce the tumble.
Action and Reaction
During the first mission. the astronauts proved they could have a "track meet'' around the lockers in the upper compartment of the workshop. By accelerating slowly, they could develop enough centrifugal force to hold themselves against the locker doors, permitting them gradually to stand up and run. The force, as it turned out. was about the same magnitude as the gravitational force the Apollo crewmen felt as they walked on the Moon. In order to accelerate around the lockers, the men pushed off from the edges of the locker doors. A 150-pound astronaut induced a very slow counter-rotation of the 200 000-pound Skylab. This reaction of the vehicle, although small. was detectable by the precisely pointed solar telescopes. While one crewman was performing solar experiments requiring fine pointing. it was necessary for the other crewman to avoid pushing off the space station walls or floors with much force. They found that they could move around very effectively with light pushes so that their motions seldom affected such experiments.
Another illustration of Newton's law was provided during the third mission. First, Pilot Pogue released three small spheres in the workshop, with virtually zero relative velocity. Commander Carr then fired the reaction control thrusters, accelerating the space station. In the films of the demonstration, the spheres appeared to move up relative to the camera. Actually, it was the camera, fixed to the Skylab, that moved away from the spheres. The expulsion of gas through the control rockets caused the space station to accelerate. The spheres, floating inside, experienced no such force and therefore remained stable in their own orbit while Skylab changed in its orbit.
Another demonstration in mechanics involved a variation of a classical mechanical oscillator. Known to some as a Wilberforce pendulum, it consisted of two masses connected by a spring. Ideally, the spring would possess only two degrees of freedom, extension and rotation. However, the spring used for the demonstration was the "Slinky" toy, a large-diameter helical coil of ribbon steel, rather than the usual helical coil of round wire. It did not possess the axial rigidity needed to demonstrate the oscillator in an ideal way. The objective was to excite oscillations in the spring-mass system along the centerline of the two masses and then to observe the energy transfer and the resultant motion change from one of translation of the masses along their centerline and alternate expansion and compression of a spring, to one of rotation of the masses about the same axis (twist of the spring).
On Earth, in a gravity environment, the energy transfer is easily demonstrated through the use of a single mass with a crossarm and masses at the ends of the crossarm to "tune" the inertia to the spring. In demonstrating the phenomenon on Skylab,....
 .....however, it was virtually impossible to obtain the desired effect. The lack of adequate axial rigidity of the spring, the difficulty in stretching the spring while maintaining its major axis along the line joining the centers of mass of the two weights, and the inability to release the two weights without inducing extraneous forces, resulted in the springmass system going "wild." The spring expanded and contracted, the masses rotated, and the whole system tumbled. However, the demonstration did provide a highly entertaining sequence of unusual motions. Conservation of momentum was undoubtedly maintained, despite the difficulty in describing the resulting motion, either verbally or mathematically.
The principle of gyroscopic motion is an application of Newton's law which states that a massive, rapidly spinning body strongly resists being disturbed and tends to react to a disturbing torque by precessing (rotating in a direction at right angles to the direction of the torque). The principle of precession has been used to develop the familiar dime-store gyroscope that will stand upright on the rim of a glass or walk a taut string. The gyroscope, however, is not merely a toy; it is a highly useful instrument. Elmer A. Sperry exploited its principles when he developed the gyroscope as a navigational device for ships and airplanes. The gyroscope is unaffected by magnetism, but it can point to true North, regardless of its surroundings. It is widely used in various aircraft instruments as a turn indicator, artificial horizon, attitude or position indicator, and in automatic pilots. Large gyroscopes provided the basic stabilization and control of Skylab's position.
Using a toy gyroscope, Commander Carr carried out an entertaining and graphic demonstration of gyroscopic principles. On January 9, 1974, he demonstrated the unstable motion of the nonspinning gyroscope as it tumbled and drifted under the influence of external forces. After spinning up the wheel, he demonstrated the effects of external forces by showing the precession at different wheel speeds and the effect of wheel speed on the stability of the spin axis. He emphasized that the precession or rotation of the spinning wheel took place only during the application of an external force and that once he removed the external force the gyroscope ceased to precess.
Carr also demonstrated that precession can be caused by friction. At high speed, the gyroscope precessed at approximately 90 degrees from the direction of the applied forces, with little wobble. At an intermediate wheel speed, a little more wobble was introduced. At very slow speed (the spokes could almost be seen going around) the resultant precession was about 20 degrees from the theoretical 90 degrees. He explained that this resulted from the friction of a straw applied to the gyroscope axle.
The fact that Carr was able to demonstrate the effects with an unsupported gyroscope greatly enhanced the performance. An excellent 1 6-mm movie film of this performance was made from the videotape record of the science demonstration and is available from NASA.