For the fourth problem of the 39th National Secondary School Physics Competition Repechage (Extended Examination), the force analysis of the four-ball system is first performed to obtain nine (non-linear differential) equations based on dynamics and kinematics to obtain two first integrals (conserved quantities). The solution is then given by numerical simulation. It is found that the original reference solution is a good approximation when the initial angular velocity is not large. Finally, the approximate solution is further investigated to obtain results accurate to t^5 in the Taylor expansion. The whole analysis provides a reference case for dealing with mechanics problems.

The phrase “moving magnetic field” which is problematic but commonly used by students is analyzed. It is pointed out that it makes no sense to say “the magnetic field is moving or static” and “a particle is moving relative to the field”. The velocity in Lorentz force and motional electromotive force is relative to the observer, and “the moving magnetic field” is in fact the moving source of magnetic field (magnet, for example). After this correction, moving source results in varying magnetic field, which induces the electric field. Thus, non-electrostatic force has not only (a component of) Lorentz force but also the induced electric field force, and the electromotive force also has two corresponding components. All these can be calculated within the acceptable range. The relativity of magnetic and electric fields is also emphasized. These analysis are helpful for students to grasp the transformation of electromagnetic field reference system.