Gyroscope

GYROSCOPE :

                           One of the most interesting areas in the science of  rotational dynamics is the

 study of spinning solid objects, tops, hoops, wheels, etc.  From the gyrocompass (which indicates

true North, rather than Magnetic North) to an understanding of how a cyclist turns corners, the

applications of this field of study are both practical and fascinating. This experiment is designed to

introduce you to some of these interesting and often counter-intuitive properties of rotating bodies.

THEORY

 A gyroscope is defined as a rigid rotating object, symmetric about one axis. Generations

of children, back at least to Greek antiquity, have found fascination in the behavior of tops, to

give the gyroscope its common name. A number of eminent physicists have also found the

complex behavior of spinning objects a matter of interest and a fit subject for detailed analysis.

More recently, very carefully engineered gyroscopes were used for navigation because the axis

of spin points in a nearly fixed direction when external torques are small. This makes the

gyroscope a good replacement for a magnetic compass, particularly in regions where magnetic

compasses are unreliable.

 EXPERIMENTAL PROCEDURE

1. Physical arrangement

                The gyroscope we will use is a solid metal sphere supported on a cushion of air, as

sketched in Fig. 3. The air cushion effectively supports the sphere under its geometric center, so

if the sphere were perfect there would be no torques acting at all. The sphere actually has a rod

fastened to it, which serves to displace the center of mass away from the geometric center of the

sphere and allow gravity to exert a small torque on the system. A sliding weight can be fastened

to the rod to adjust the torque as desired. The rod also serves as a convenient marker for the axis

of rotation, and a handle for manipulating the gyroscope. A secondary jet of air is available to

spin the sphere very rapidly.

 There are a number of precautions which you must be aware of to avoid problems for

yourself or the apparatus. The rod is strong enough to support the heavy sphere only in the

vertical position, so avoid picking up the sphere by the rod if at all possible. The sphere itself is

rather soft metal and it must be exactly round for the experiment to work. It will, therefore, be

ruined if it falls onto the hard floor. Finally, you will be working with a rapidly spinning object.

If the spinning ball contacts the supporting cup it will probably climb out and proceed across the

room, damaging itself and perhaps also you. You can avoid this problem by leaving the air

supply on whenever the sphere is spinning, and by not pushing the sphere into the support. The

rod has a bearing on the end which you can hold to control the sphere without slowing it down.

When you do want to slow the rotation, gently squeeze the rod with two fingers, while holding

onto the bearing to steady it. Do not push directly on the sphere. With a little care and common

sense you should not have any problems.

2. Qualitative observations

 Begin your work by turning on the air supply so that the sphere floats. You may have to

lift the sphere slightly to start the flow. If the sliding weight was left on the rod, set it aside for

later use. Holding the rod vertically with your fingers on the bearing, twirl the rod between the

fingers of your other hand to start the sphere spinning. You can now tilt the rod to any desired

angle and release it to observe the precession and nutation.

Try this for a few different angles. Try also to see the effects ofreleasing the rod from rest, when moving at about the precession speed, and when moving in the opposite direction. It may help to think of the tip as marking a point on the surface of a sphere. The precession then corresponds to tracing a circle of constant latitude and the nutation is a small deviation from the circularpath. The resulting motion is complicated, so this will be a real challenge to your obser- vational skills. Describe the motion of the tip of the rod for various conditions as best you can, perhaps with the aid of a sketch.

As noted in the theory section, the motion of a slow top is quite distinctive. You can demonstrate this by spinning the sphere with the rodvertical and then releasing it. Start out with a rapid rotation, for which the motion is a slow precession, and then slow down the rotation by gently grasping the rod between your fingers while holding onto the bearing. Decrease the rate of spin in several stages, releasing the rod to observe the motion after each decrease. Describe the motion. Is it still reasonable to approximate the motion as a uniform precession plus a small nutation?

3. Quantitative analysis

The quantitative part of this experiment consists of checking two ofthe predictions of Eq. 6. We expect ! to depend directly on rmg, and inverselyon !. Since we can vary both of these, we can check the prediction. For an accurate test we need to spin the sphere quite rapidly, so we will use an air jet.Hold the rod horizontal, grasping just the bearing, and direct the air at the equator of the sphere. After three or four minutes the sphere will be spinning quite rapidly. If you now set the jet aside and release the rod, thegyroscope will precess slowly. You can measure the time for a completeprecession with a stopwatch, using some convenient reference for the start and stop points. Of course, the rate of spinning will decrease with time, but the friction is small enough that this process is slow.

To measure the spin velocity we will use a strobe light. Position the strobe so that it will brightly illuminate the sphere, but not so close that it will interfere with the motion. When the interval between flashes is exactly the same as the time for one rotation of the sphere, the rotational motion will appear to be "stopped", because the same parts of the sphere will be in the same place ateach flash. The sphere has been marked with two black lines to make it easierto tell when it is "stopped". By measuring the time interval between flashes when this condition is met, we determine the period of the spinning motion.