Lecture Demonstration Apparatus
Apparatus Title: A Low Cost, Battery-Powered, Precession Demonstrator Which Permits Extended Periods of Student Manipulation
Abstract : A 9 Volt battery-powered motor keeps the flywheel spinning at high speed, allowing each student, as well as the instructor, to push on the shaft with a pencil and observe that the shaft precesses at right angles to the push. A second motor provides a low friction vertical axis.
2001 AAPT Apparatus Competition, Rochester, N. Y. Lecture Demonstration Apparatus
Apparatus Title: A Low Cost, Battery-Powered Precession Demonstrator Which Permits Extended Periods of Student Manipulation
Abstract (40-50 words) A 9 Volt battery-powered motor keeps the flywheel spinning at high speed, allowing each student, as well as the instructor, to push on the shaft with a pencil and observe that the shaft precesses at right angles to the push. A second motor provides a low friction vertical axis.
Description of Apparatus:
The apparatus described here is used to demonstrate the precession that results when a torque is applied to an object at right angles to its angular momentum. A motor spins a flywheel at high speed, giving it an angular momentum along the shaft of the motor. The motor can be reversed to reverse this direction. The observer then holds a pencil at each end and pushes its center gently against the sleeve at the end of the shaft. This applies a torque at right angles to the shaft. Surprisingly (to the novice student), the sleeve end of the shaft does not move the way it is pushed, but at ninety degrees to that direction. The push can be up or down, or toward or away from the observer, or, for that matter, in any direction perpendicular to the shaft. The effect is explained in most introductory physics texts, such as that by Halliday, Resnick, and Walker. Briefly, the incremental change in angular momentum is in the direction of the torque, which is perpendicular to the initial angular momentum. This perpendicular change in the angular momentum changes the direction, but not the magnitude, of the angular momentum. The situation is not entirely unlike that in which the centripetal force changes the direction, but not the magnitude, of the linear momentum of an object in uniform circular motion. In figure 1, the slide switch indicates a direction of rotation which gives an angular momentum pointing to the left. The pencil is pushing into the page, giving a torque which is directed upward. This would make the angular momentum point more upward, and cause the sleeve end of the shaft to move downward.
I find the apparatus described here to be highly satisfactory for demonstrating precession in a way that allows students to see and feel the directions of the angular momentum and the torque. Its greatest virtue is its motor-driven flywheel. Since the flywheel maintains a high speed for extended periods of time, there is no time lost restarting it, and the effects being demonstrated do not weaken as the flywheel slows (unless you choose to turn the motor off to observe this).
In small classes, there is time to demonstrate what to do and then to allow each student to actually feel the effect. This is much more effective than a demonstration by the instructor. For a large lecture class, the apparatus could be enlarged for better viewing, but the cost is so low that one would be well advised to provide enough devices so that every student could personally experience the effect.
A key element in the success of the apparatus is a low-friction vertical axis of rotation. This is achieved at very low cost by using a second motor. There are no electrical connections to this motor; it simply provides a good, low-cost, low-friction bearing. The effectiveness of the demonstration is also improved by the provision of a plastic sleeve on the end of the shaft, against which the observer presses a pencil. Because the sleeve can rotate as the shaft moves along the pencil, there is very little frictional torque due to this motion. The near elimination of these frictional torques makes the demonstration much cleaner.
Also essential, is a means of adjusting the balance and stability of the horizontal shaft. For commercial production, one would want to provide nut and screw arrangements similar to that used to zero balances, one along the length of the shaft and one at a right angle to it vertically. In my simplest of all arrangements, these adjustments are made by moving the 9 Volt battery. It is slid in or out until balance is achieved. Then stability is tested by tipping the shaft away from the horizontal. If it stays tipped either way you tip it, then the balance is unstable, and the battery needs to be moved downward. If it quickly returns to the horizontal, then it is too stable, and the battery needs to be moved upward. The shaft should return to the horizontal, but just barely. This will minimize the gravitational torque when the shaft is tipped.
Another important feature is the DPDT three-position switch used to turn the motor on or off and to reverse its direction. The switch is arranged so that it moves in the direction that the angular momentum vector points. Also, the direction of rotation is prominently marked at each end of the switch. With the motor spinning at high speed, it would be difficult to tell which way it is turning without these indicating arrows.
Figure 2 is only approximately to scale. The actual dimensions are not important. One might have to make adjustments to achieve balance, even if the dimensions of the original were reproduced exactly, due to variation in part masses. My apparatus is about 30 cm tall and the horizontal shaft is about 35 cm long.