Groscopio

Laws of gyroscopes / 3-axis gyroscope

LEP 1.3.19 -00

Related topics Momentum of inertia, torque, angular momentum, precession, nutation Principle The momentum of inertia of the gyroscope is investigated by measuring the angular acceleration caused by torques of different known values. In this experiment, two of the axes of the gyroscope are fixed. The relationship between the precessionfrequency and the gyro-frequency of the gyroscope with 3 free axes is examined for torques of different values applied to the axis of rotation. If the axis of rotation of the force-free gyroscope is slightly displaced, a nutation is induced. The nutation frequency will be investigated as a function of gyro-frequency. Equipment Gyroscope with 3 axes Light barrier with Counter Power supply 5 V DC/2.4 AAdditional gyro-disc w. counter-weight Stopwatch, digital, 1/100 sec. Barrel base -PASSSlotted weight,10 g, black Slotted weight, 50 g, black Holder for slotted weights Fig. 1: 3 axis gyroscope.

Tasks 1. Determination of the momentum of inertia of the gyroscope by measurement of the angular acceleration. 2. Determination of the momentum of inertia by measurement of the gyro-frequency andprecession frequency. Investigation of the relationship between precession and gyro-frequency and its dependence from torque. 3. Investigation of the relationship between nutation frequency and gyro-frequency. Set-up and procedure 1. To start with, the polar momentum of inertia Ip of the gyroscope disk must be determined. For this, the gyroscope is fixed with its axis directed horizontally andpositioned on the experimenting table in such a way that the thread drum projects over the edge of the table (Fig. 2). The thread is wound around the drum and the accelerating mass m (m = 60 g; plate with 5 slotted weights) is fastened to the free end of the thread. Several experiments are carried out for different drop heights h of the accelerating mass, from which the corresponding average falling timetF from the moment the gyroscope disk is released until the mass touches the floor is determined. The diagram of t 2 versus h is plotted and the moment of inertia of F the gyroscope disk is determined from the slope of the straight line (Fig. 3).

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PHYWE series of publications • LaboratoryExperiments • Physics • © PHYWE SYSTEME GMBH & Co. KG • D-37070 Göttingen

P2131900

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LEP 1.3.19 -00

Laws of gyroscopes / 3-axis gyroscope

2. The gyroscope, on which no forces act, and which can move freely around its 3 axes, is wound up and the duration tR of one revolution (rotation frequency) is determined by means of the forked light barrier, with the axis of the gyroscope lyinghorizontally. Immediately after this, a mass m* = 30 g is hung at a distance r* = 27 cm into the groove at the longer end of the gyroscope axis. The duration of half a precession rotation tP /2 must now be determined with a manual stopwatch (this value must be multiplied by two for the evaluation). The mass is then removed, so the gyroscope axis can regain immobility, and tR can be determined again.The inverse of the average value from both measurements of tR is entered into a diagram above precession time tp. In the same way, the other measurement points are recorded for decreasing number of gyroscope rotations. The slope of the resulting straight line allows to calculate the momentum of inertia of the gyroscope disk (Fig. 6). 3. If a slight lateral blow is given against the axis of therotating gyroscope on which no forces are acting, the gyroscope starts describing a nutation movement. The duration of one nutation tN is determined with the manual stopwatch and this is plotted against the duration of one revolution tR, which is again determined by means of the forked light barrier (Fig. 7).

According to the law of action and reaction, the force which causes the torque is...