An inertial reference frame and another reference frame have a common origin O. rotates with constant angular velocity with respect to . Assuming the result that
for an arbitrary vector , show that
where is the position vector of a point measured from the origin.
A system of electrically charged particles, all with equal masses and charges , moves under the influence of mutual central forces of the form
In addition each particle experiences a Lorentz force due to a constant weak magnetic field given by
Transform the equations of motion to the rotating frame . Show that if the angular velocity is chosen to satisfy
and if terms of second order in are neglected, then the equations of motion in the rotating frame are identical to those in the non-rotating frame in the absence of the magnetic field B.