In the book Surely You Are Joking, Mr. Feynman! Richard Feynman tells a story of a Cornell cafeteria plate being tossed into the air. As the plate spun, it wobbled. Feynman noticed a relation between the two motions. He solved the motion of the plate by using the Lagrangian approach. This solution didn’t satisfy him. He wanted to understand the motion of the plate by analyzing the motion of its individual particles and the forces acting on them. He was successful, but he didn’t tell us how he did it. We provide an elementary explanation for the two-to-one ratio of wobble to spin frequencies, based on an analysis of the motion of the particles and the forces acting on them. We also demonstrate the power of numerical simulation and computer animation to provide insight into a physical phenomenon and guidance on how to do the analysis.

Equatorial noise emissions (fast magnetosonic waves) are electromagnetic waves observed routinely in the equatorial region of the inner magnetosphere. They propagate with wave vectors nearly perpendicular to the ambient magnetic field; that is, they are limited to frequencies below the lower hybrid frequency. The waves are generated by instabilities of ring-like proton distribution functions, which result in their fine harmonic structure with intensity maxima close to harmonics of the proton cyclotron frequency in the source region. Although most equatorial noise emissions are continuous in time, some events exhibit a clear quasiperiodic time modulation of the wave intensity, with typical modulation periods on the order of minutes. We analyze 72 such events (17 observed by the Cluster spacecraft, 55 observed by the Van Allen Probes spacecraft) for which high-resolution data were available. The analysis of the observed harmonic structure allows us to determine source radial distances of the events. It is found that the calculated source radial distances are generally close to the radial distances where the events were observed. The harmonic numbers where the events are generated range between about 12 and 30. Two events for which the spacecraft passed through the generation region were identified and analyzed. No simultaneous ultra-low-frequency magnetic field pulsations and no periodic plasma number density variations were observed. Although the in situ measured proton distribution functions were shown to be responsible for the wave growth, an insufficient resolution of the particle instruments prevented us from detecting a quasiperiodic modulation possibly present in the particle data.