Question: Show that the areal velocity is constant for a particle moving under the influence of an attractive force given by F(r) = -kr. Calculate the time averages of the kinetic and potential energies and compare the results of the viral theorem.
Areal velocity w = (r * V)/2
Where * denotes the vector product, r is the position of the particle and V its velocity.
This solution provides step by step calculations for time averages of kinetic and potential energies.