Journal of Technical Physics, J. Tech. Phys., 46, 2, 107–115, 2005. Polish Academy of Sciences, Institute of Fundamental Technological Research, Warszawa. Military University of Technology, Warszawa.

ANOMALOUS MOVEMENT RESISTANCE IN A SPINNING GYROSCOPE J. M A Z U R 1 ,

J. S P A L I Ń S K A–M A Z U R

2

and

J. R Y R Y C H

1

Jagiellonian University Faculty of Chemistry Ingardena 3, 30-060 Kraków, Poland 2

University of Opole Plac Kopernika 11, 45-040 Opole, Poland

A symmetric harnessed gyroscope accelerated to a given spinning frequency takes different time periods to stop, depending on the direction of previous spins. For repeated alternating, anticlockwise and clockwise spinning, the rotation period in both directions significantly increases, which is not the case when the gyroscope is repeatedly rotated in the same direction. Using the measurements it was observed, that the time of gyroscope’s rotation was significantly lengthened or shortened, what indicates that it either increased or decreased the movement resistance of the gyroscope. The presented experimental results suggest the existence of anomalous movement resistance and demonstrate that a fixed spinning gyroscope displays unusual history-dependent movement resistance effects. The effect is real, large, reproducible and does not follow from experimental errors. Key words: spinning gyroscope, movement resistance, clockwise rotation, anticlockwise rotation.

1. Introduction

The gyroscope and the spinning top are among the most thoroughly investigated physical systems ([1–5]). However, little attention has been paid to the constrained spinning top. We wish to report anomalous rotational behaviour in a symmetric gyroscope, the axis of which is held vertically in a frame (so that no precession is possible) and rotated at low frequencies (tens of Hertz). 2. Experimental

A disk was threaded on a spindle, in such a way that the centres of gravity of the disk and the spindle coincided, and placed vertically in an aluminium frame (Fig. 1). The spindle was sharpened to a fine point at both ends and rested on a needle bearing at the bottom of the frame; at the top its horizontal motion was similarly restrained. The entire apparatus was placed on a horizontal vibration-free stone slab, and maintained at 22◦ C in a draft-free environment remote from moving masses, magnetic objects and other external influences.

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Fig. 1. The spinning top system used in the experiments. The gyroscope in frame is attached to a base. The axis of rotation is normal to the base.

The experiments consisted of accelerating the gyroscope, with a stream of compressed air directed at its circumference, to a constant frequency, which was monitored electronically, and measuring the time required for the gyroscope to come almost to a stop. The measuring system consisted of a light source directed at the surface of the rotating disk (to which were attached two reflecting spots located opposite each other), a 75 kHz frequency generator, a sensor, a 16-bit counter and a gating system driven by the sensor. The gate was opened and closed by every second reflecting spot, and the generator signal was counted by the sensor during the time the gate was open. The result of the count, x, over a single revolution of the top is related to the period of rotation as T = x/75000, and to the frequency as f = 1/T = (75000/x) Hz. Since the error of the counter was ∆x = ±1 and that of the generator was negligible, ∆f /f = ±2f /75000. Thus the rotational frequency of 32 Hz was measured with error less than 0.08%. The measurement error of the time was ∆t = 0.02 s. The lowest frequency which could be measured (corresponding to counter overload) was 1.144 Hz. We accelerated the top to 33 Hz, 29 Hz over ca. 20 s, and then measured the time required for the gyroscope to slow down from the initial frequency of f = 32 Hz, 28 Hz to 2.5 Hz (not to zero, in order to avoid random friction-dominated effects at very low frequencies). The spinning frequency and the time were recorded once for every revolution of the top, which means that each of our plots (Figs. 2–6) corresponds to several hundred experimental points.

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Fig. 2. Measurement 1. Time evolution of the number of series. Teflon disk (mass 47.60 g) supported on a steel spindle (23.46 g) and a steel bearing. (a) LRLR . . . rotation: series 1, 2, . . . , 23; (b) The final part of the RRRRR; LLLLL rotation: series alternately 24, 25, . . . , 28; 29, 30, . . . , 33; the small differences in spin times; in the early part of this graph various plots almost exactly coincide.

Fig. 3. Measurement 1. Time evolution of the number of series. Teflon disk (47.60 g) supported on a polyamide spindle (3.21 g) and a polyamide bearing. (a) LRLR. . . rotation: series 1, 2,. . . , 7. (b) The final part of the RRRR; LLLL rotation: series 8, . . . , 11; 12, . . . , 15; the small differences in spin times; in the early part of this graph various plots almost exactly coincide.

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Fig. 4. Measurement 1. Time evolution of the number of series. Brass disk (242.94 g) supported on a steel spindle (23.46 g) and a steel bearing. (a) LRLR. . . rotation: series 1, 2, . . . , 16; (b) The final part of the RRRR; LLLL rotation: series alternately 17, . . . , 20; 21, . . . , 24; the small differences in spin times; in the early part of this graph various plots almost exactly coincide.

Fig. 5. Measurement 2. Time evolution of the number of series. Teflon disk (mass 177.32 g) supported on a polyamide spindle (3.21 g) and a polyamide bearing with clockwise (right) rotation. The running time from the initial frequency of 32 Hz to 2.5 Hz. After the first measurement, the rotor was turned (together with the frame and the bearings) with the drive to the horizontal axis (upside down position) and a series consisting of five measurements were done; then the frame was turned to the initial position the same as for the first measurement and four serie were done. The measurement error of the time was ∆t = 0.02 s.

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Fig. 6. Measurement 3. Time evolution of the number of series. Brass disk (mass 516.54 g) supported on a steel spindle (23.46 g) and a steel bearing with clockwise (right) rotation. The number of first series after the rotation with the additional element placed on rotor’s spindle: 2, 8, 14. The running time from the initial frequency of 28 Hz to 2.5 Hz. The measurement error of the time was ∆t = 0.02 s. 3. Results

A series of measurements was made – first of the different rotation directions, the second with the opposite positions of the gyroscope and the third after the rotation with the additional element fastened to the gyroscope’s spindle. The discussed measurements had to prove the existence of the movement parameters that were not taken into account in the dynamics of the rigid body or skipping the inner interaction with considerable influence on the movement of the rigid body. 3.1. Measurement 1. In the first series of experiments, a Teflon disk with a mass of 47.68 grams was spun alternately anticlockwise (left), L, and clockwise (right) direction, R. Successive experiments were performed at 10 minute intervals, so that there was no frictional heating of the bearings or spindle. We have found that the gyroscope ran in different directions for very different time periods, depending on the direction and number of previous spins. Further, the effect of alternate spinning directions was cumulative. Thus Fig. 2(a) shows that when a Teflon disk with the spindle (the spindle mass: 23.46 grams) and bearing made of hardened steel was spun once only in the anticlockwise direction (which we denote L1 ), it took 160.8 s to reach 2.5 Hz. However, when the same gyroscope was spun LRLRLRLRLR [denoted to (LR)5 ], on the last run it took 304.3 s to reach the same final speed. For (LR)6 L1 rotation, the gyroscope reached final speed in 318.6 s, almost exactly twice as long as in the first run. It thus appears that the lengthening of the spinning period is produced by changing the direction of spin.

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To confirm this, we performed a second series of experiments with the gyroscope previously used in the first series. The gyroscope was spun repeatedly, but not alternately, in the clockwise and the anticlockwise directions. Fig. 2(b) shows that the result of the first clockwise rotation, R1 , was 345.5 s and of the fourth, R4 , 324.4 s, a decrease of 6.1%. The direction of spin was then reversed. The first anticlockwise rotation, R4 L1 , gave 325.9 s, and the fourth, R4 L4 , 307.4 s, a decrease of 5.7%. Note that the initial rotation times in the second series of experiments follow closely the final times in the first series, pointing to a kind of “memory” movement resistance, which we found to persist for times of the order of tens of hours. We believe that the small differences between the times of R and L rotations in the second series are due to the fact that the gyroscope “remembers” the first series of experiments. We performed further experiments in order to investigate the role of the material used for the construction of the gyroscope and its support. The L1 rotation of a Teflon disk supported on a light Ertalene PA6 polyamide spindle (the polyamide spindle mass: 23.46 grams) and bearing took 105.92 s, while the (LR)3 L1 rotation lasted 219.63 s more than twice as long (Fig. 3(a)). These times are proportionally shorter than in the first two series of experiments because of the greatly reduced mass of the spindle (3.21 g as opposed to 23.46 g). Note also that the light gyroscopic system doubles its rotation time much sooner (after seven series of spins) than the heavier system (13 spins). As before, repeated rotation of the gyroscope in the same direction has a very small effect on the rotation times (Fig. 3(b)). Experiments with a massive brass disk with a mass of 242.92 grams on a steel spindle and steel bearing confirm our findings. The L1 rotation took 190.7 s and the (LR)8 rotation 290.2 s (Fig. 4(a)). We observe that more spins are required for the heavy gyroscopic system to reach the same result as the less massive ones. To confirm the role of alternate spinning directions, we “turned over” the disk of the brass with steel spindle by rotating it 180◦ around a horizontal axis and replaced it on the steel axle without changing the orientation of the axle or bearing. Thus, the gyroscope and bottom surfaces of the rotor were interchanged. We then rotated the gyroscope RRRRLLLL (Fig. 4(b)). We see that the spinning times return to the initial times in the LRLR. . . series, indicating that when the disk is turned over, the gyroscope “forgets” its earlier movement resistance history. Subsequent runs in the same direction resulted in very small changes of spinning times.

3.2. Measurement 2. A series of measurements for the clockwise rotation on a gyroscope consisting of a Teflon disc with a mass 177.31 grams on the polyamide spindle (3.21 grams) and bearings was made to examine the influence of the bearings on the anomalous movement resistance and “memory” effect. After the first measurement, the rotor was turned (together with the frame and the bearings) with the drive to the horizontal axis (upside down position) and a series consisting of five measurements were done; then the frame was turned to the initial position the same as in the first measurement and four series of measurements were done. All the measurements were done for the same initial frequency (32 Hz) and for the same type of rotation – the clockwise one – maintaining the same ten minutes intervals between them. The first and the seventh measurements were the subsequent measurements on the same bearings and at the same position of the rotor. During the measurement series the bottom bearings were

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far more burdened (Fig. 5) than the upper ones which during the first and the seventh measurements functioned as a bottom bearing. The running time of the free rotation (from the initial frequency of f = 32 Hz to 2.5 Hz) for the first, seventh and the eighth measurements was 114.01 s, 412.11 s and 486.33 s (Fig. 5). 3.3. Measurement 3. The following series of the measurements was made: (1) – measuring of the time of the movement and the frequency of a rotor on the steel axis for clockwise direction and the initial frequency of 28 Hz; (2) – an additional element was fastened to rotor’s spindle over the rotor’s disc – the rotor was propelled to the frequency of 29 Hz and then let free – when it stopped, the additional element was taken off the spindle; (3) – the initial measurements were repeated several times. All the measurements were done for the same initial frequency and for the same type of rotation – the clockwise one – maintaining the same ten minutes intervals between them. Once the times of the movements of the gyroscope become stabilized, the procedure (2) was repeated with the additional element of different parameters and placed below the rotor’s disc, and then the procedure (3) was followed. Then the whole experiment was repeated with the additional element (different, but of identical parameters) placed over the rotor’s disc. An additional element (45 grams) was mounted on the gyroscope’s steel spindle over the rotor’s brass disk (the disk mass: 516.54 grams; the steel spindle mass: 23.46 grams). The measurements after the rotation with the additional element placed on rotor’s spindle show considerable differences between the running times. The first, third measurement’s result of running time from the initial frequency of f = 28 Hz to 2.5 Hz was 259.93 s, 453.72 s (Fig. 6). 4. Discussion

A spinning gyroscope slows down and stops because of frictional forces between the spindle and the bearings. These forces are due to microscopic irregularities in the surfaces involved, and we needed to address the possible role of effects such as wear and tear, or surface rearrangement of the bearing or spindle, leading to reduced friction. Given the results of the experiments described above, we believe that although friction is responsible for the gyroscope ultimately coming to a stop, frictional effects cannot be responsible for the effects observed. First, to a stop, frictional effects cannot be responsible for the effects observed. First, they would depend on the type of material of the spinning disk, spindle or bearing. Second, needle bearing wear would reduce the rotation times (the spindle’s top is being rubbed away which causes the moment of friction to rise) and not lengthen them, while surface rearrangement would not favour alternate directions of rotation, but would affect all the results equally. For the same reason, our findings cannot be explained in terms of these frictional (microscopic irregularities) force, because such forces would lead to a constant difference between rotations in the anticlockwise and in the clockwise directions, which is clearly not the case. Additionally, the time differences for the anticlockwise and clockwise rotations are large at the beginning of measurements, they decrease as the time of gyroscope’s movement rises i.e. in the subsequent experimental runs. It seems to be obvious that the bearing’s microscopic irregularities would generate an opposite effect. Neither did we observe any vibration of the gyroscope or its frame. Again, such vibrations would affect rotations both in the clockwise and in the anticlockwise directions, but would not change the relationship between the two sets of results.

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The “memory” movement resistance effect is well observed for the low resistances of the rotor movement – so there is a factor proportional to the movement resistance which reduces the effect and even can eliminate it. To sum up, it could be concluded that the effects are not only linked to the bearings. The changes of the friction forces of the bearings or the inner friction can not accumulate during inner friction in any other way than as a thermal energy or the changes of the inner structure. The observed differences of rotor’s temperature were about 0.1 grades. During the measurements the outside changes of rotor’s structure were not observed; the inner changes of rotor’s structure seem to be little probable due to low values of the inertia forces connected with low value of the rotation frequency, far lower than the structural inner forces in the solid. Between the measurements, the rotor was left motionless for 10 minutes to prevent the accumulation of the thermal energy both in the rotor and the bearings, to eliminate its influence on the following measurements. For the first and the seventh measurements (Measurement 2), the time of the free rotation was longer by a factor of 3.61, despite the fact that the movement took place under the same conditions (Fig. 5). Thus, it means that the effect of anomalous resistance does not depend on the changes of friction forces in the bearings. From the point of view of the material of the rotor the clockwise rotation of the gyroscope in the position from second to sixth measurement corresponds to the anticlockwise rotation of the gyroscope in the position of the first and the seventh measurements. Therefore, these measurements are analogical to the measurement series of the previous RLLLLLRRRR type. The considerable differences of the movement times between the first and the seventh measurement show rather that occurrence of the anomalous movement resistance is connected with interaction of the inner substance of the rotor and not with the changes of the bearings friction. The measurement series with the same rotation type show very weak changes of motion resistance (we observe very small differences in time periods of motion). This is in contrast to the results of measurement series where the rotation type was subject to cyclic changes (LRL. . . series – Measurement 1). In this case, substantial variation of motion resistance was observed (i.e. time periods of motion considerably differed from each other). The forces of internal and external friction do not depend on the type of rotation; therefore, they cannot be responsible for the observed differences of gyroscope’s motion resistance. The measurements after rotation with the additional element (Measurement 3) mounted on the spindle show considerable differences (74.55% of the difference between the running times of the first and third measurements), despite the same conditions in which the movement took place (Fig. 6). After the measurements were done, it was observed that the time of gyroscope’s rotation was significantly lengthened or shortened, which indicates the fact that it either increased or decreased the movement resistance of the gyroscope. It shows the accumulation of some kind of energy of rotor’s elements during the rotation, seating of the bearings and in the frame itself, so in the elements of a considerable mass, contrary to the small mass of the bearings. The considerable differences of the movement times between measurements show rather that the occurrence of anomalous movement resistance is connected with interaction of the inner substance of the rotor, gyroscope’s frame, the seating of bearing and the additional element. If the change of the movement resistance in a spinning gyroscope depended on the frequency, then for a gyroscope in a frame accelerated to a certain frequency and released freely, there should occur differences in energy emission rates between the previous rotation. The experiment confirms this anticipation.

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Summing up, the experimental effects observed confirm the anticipation that a spinning gyroscope has anomalous movement resistance. Our experiments demonstrate that a fixed spinning gyroscope displays unusual history-dependent effects. Although we are at present unable to explain our results, we are confident that the effects we describe are real, large, reproducible and are not caused by experimental errors. The discussed experiment had to prove a gap between the theory and the practice and to show that the bearings cannot be responsible for it. They can be easily tested anywhere at low cost. This anomalous movement resistance effects in a spinning systems should be examined empirically as well as theoretically, in order to find an explanation of this phenomenon, since it gives enormous possibilities of technical applications. We believe that, given the considerable potential practical applications, these results deserve careful systematic examination. References 1. W.D. MacMillan, Dynamics of rigid bodies, Macmillan’s Theoretical Mechanics, Dover, New York 1960. 2. C. Kittel, W.D. Knight, M.A. Ruderman, Mechanics, Berkeley Physics Course, McGrawHill, 1, New York 1965. 3. L.D. Landau, E.M. Lifshitz, Short course of theoretical physics, Nauka, Vol. 1, Moscow 1969. 4. H. Goldstein, Classical mechanics, Addison-Wesley Series in Physics, Addison-Wesley, Reading, Mass., London 1980. 5. A.P. Arya, Introduction to classical mechanics, Prentice Hall, Upper Saddle River, N.J. 1998.

Received July 1, 2004.