Rotating wheel in suitcase

A video of this demonstration is available at this link.

The disc of a pneumatic sander (at left in the photograph above) is used to get the large wheel inside the suitcase spinning. This rather noisy process takes a few minutes. To avoid revealing what is inside the suitcase until the class has had a chance to observe the rather strange behavior of the suitcase, it is best to have it prepared behind the scenes and then slipped into the lecture hall via (one of) the access door(s). Once you have shown the class what happens when you try to turn the suitcase in either direction, you can then undo the latch and open it to reveal the spinning flywheel to them. The flywheel bearing is fairly good, and the wheel can spin for perhaps about 20 minutes, but the rotation does decay, so it is best to have some idea of when you will need this demonstration during your class, and to have it prepared five or ten minutes before then. Oriented as in the photograph above, the flywheel spins in a clockwise direction. So its angular momentum vector, L, points away from the cover, that is, along the axle of the flywheel, from the cover toward the solid back of the suitcase. (An arrow on the top surface of the suitcase now shows the direction of L.)

Assume that you give the suitcase to a student, who grasps it with the right hand, hinged cover facing outward. If the student walks in a straight line, the suitcase follows without any odd effects. If the student attempts to make a left turn, the bottom of the suitcase swings inward, toward the student. If the student makes right turn, the bottom of the suitcase swings outward, away from the student.

This is similar to what happens with a spinning top, or a gyroscope mounted on a pivot and allowed to precess, which is what happens in the rotating bicycle wheel demonstrations (28.54 -- Bicycle wheel as a top, and 28.57 -- Bicycle wheel precession). As noted above, the flywheel in the suitcase has an angular momentum vector that points perpendicular to the broad faces of the suitcase, from the cover toward the back of the case. In taking the suitcase around a left turn, the student is trying to change the angular momentum vector by rotating it to the left (counterclockwise). It is possible to do this, but it requires the application of a torque, τ = dL/dt. If we imagine how L points at the beginning of the turn and a short time after (dt), we can see that the change in angular momentum, dL, points horizontally, facing backward (from the student’s perspective). The right hand rule tells us that this torque is counterclockwise, that is, the student must push outward on the bottom of the suitcase to keep it vertical. Without the application of this torque, the bottom of the suitcase twists inward, toward the student.

Now, we have the student try to take the suitcase around a right turn. This time, dL points forward, which means that the torque to keep the suitcase vertical must be clockwise. In the absence of this torque, the bottom of the suitcase moves outward.

Perhaps if the handle of the suitcase were a vertical rod, or the student could grasp the suitcase at both top and bottom, it would be possible for the student to provide the appropriate torque to keep the suitcase vertical. With the single loop handle at the top, however, this is nearly impossible to do, and it makes for an entertaining demonstration.

The angular momentum of the flywheel, L, is Iω, where I is the moment of inertia of the flywheel and ω its angular velocity, dθ/dt. (See 28.03 -- Mounted bicycle wheel.) If we call the angle through which L turns as the student attempts to turn the suitcase φ, then in a short time dt, L turns through an angle . Since is small, we can also calculate the magnitude of the torque (if we know L and how fast it is changing direction) by: τ = dL/dt = (L sin )/dt. For small φ, dL is perpendicular to L, so dL = L sin . Also, for a small angle, sin = , so τ = L dφ/dt, or .

An analogy that may aid understanding of the physics of this demonstration is one that you can draw between the torque necessary to change the angular momentum of the suitcase flywheel, and the inward radial force necessary to make an object move in a circle instead of a straight line. In the latter case, one must change the linear momentum, p, of the object, but leave its magnitude unchanged. If we take the tangential velocities of the object before and after a small time interval dt, and call them v1 and v2, we see that dv, (= v2 - v1), and thus dp, points radially inward, perpendicular to the instantaneous linear motion of the object. For the suitcase flywheel, as we saw above, we are trying to change the direction of the angular momentum, L, but leave its magnitude unchanged. If we take this change in direction of angular momentum, dL, over a small time interval dt, we find that it points at right angles to L, so the torque we must apply to accomplish this is perpendicular to L. You can read (from a UCSB-linked computer) a short paper about this analogy here.

Some humor:

Given the odd behavior of the suitcase in this demonstration, it would not be surprising if someone used a similar device as the basis for a practical joke. I have found several references to such a prank, involving three different physicists!

George Gamow, in his book Gravity (pp. 75-76), writes of Jean Perrin having packed a running aviation gyroscope inside a suitcase and then checking it at a Paris railroad station. A porter then picked it up and began carrying it through the station. When he tried to turn a corner, the suitcase, of course, refused to follow, instead turning at an unexpected angle. Shouting “Le Diable soi-même doit être la-dedans!” (“The Devil himself must be inside!”), he dropped the suitcase and ran. David Darling also relates this story here.

Resnick and Halliday (Physics, Part 1, p. 274), Jearl Walker (The Flying Circus of Physics, p. 53) and Bill Sones and Rich Sones, Ph.D. (several places on the web, among them here) tell a story about Robert W. Wood of Johns Hopkins, who spun up a massive flywheel and enclosed it in a suitcase. Resnick and Halliday have him giving it to a porter with instructions to follow him. The others have him leaving it for the porter to pick up. When he picked it up, the porter noticed the rather heavy weight of the suitcase, but nothing else particularly extraordinary until he tried to round a corner with it, at which point the suitcase moved in a rather strange way. Frightened, he dropped the “possessed” suitcase and ran away.

A page that used to be on the web site of Clark University had a story about Arthur Gordon Webster, who had been a professor there, which noted that physicists always enjoyed meeting Webster when he arrived at railroad stations because of his penchant for playing practical jokes of a scientific nature. Webster had constructed a portable, battery-powered gyroscope housed in a suitcase, which he took with him on his travels. As his train was coming into the station, he would start the gyroscope, which would then be up to speed by the time the train stopped at the station. He would then hand it to a porter, telling him to take good care of it. Then he would walk briskly down the station platform, making abrupt turns as he went. As the porter attempted to follow him, however, the suitcase would make all sorts of crazy motions, leaving the porter desperately hanging on, and his colleagues laughing hysterically.

This collection might lead one to believe either or both of two things: that the stories are apocryphal, and that physicists enjoy playing practical jokes. In either case, they are delightfully amusing, as is this physics demonstration.

References:

1) Resnick, Robert and Halliday, David. Physics, Part One, Third Edition (New York: John Wiley and Sons, 1977), pp. 262-263.
2) Kittel, Charles; Knight, Walter D. and Ruderman, Malvin A. Mechanics/Berkeley Physics Course – Volume 1 (New York: McGraw-Hill Book Company), pp. 255-257.

Hyperlinks embedded above, but whose URLs are not listed above, for the stories of practical jokes:

1) http://www.daviddarling.info/encyclopedia/S/scientific_practical_jokes.html
2) http://www.readthehook.com/85043/strange-true-polar-bare-icy-swim-just-battle