Some Physics

 Mike Gilmore, a former colleague has been kind enough to send me a few physics problems to work out. The harmonic motion problems helped me remind myself that in harmonic motion omega is everything, or nearly.  The orbital motion problems were a bit further removed from my usual thoughts but omega is nearly as important in them.  In circular motion the acceleration is equal to omega ( the angular velocity -radians per second) squared times the amplitude and the direction of the acceleration is opposite the displacement. Any other motion where the acceleration can be expressed as  some constant times the amplitude, i.e. a = const x Displacement and is in the direction opposite to the displacement yields an angular velocity, omega,  = square root of the constant . The frequency simply equals
omega /2pi and the period = 1/frequency = 2 pi/omega.

Orbital  motion introduces gravitational potential energy and conservation of angular momentum into the mix, but if the motion is circular omega is still a useful quantity, and omega Rsquared is conserved.