Velocity Change Calculation for an Object Moving on a Rotating Spherical Surface

Jean C. Piquette

Retired physicist from Naval Undersea Warfare Center and current Fellow of the Acoustical Society of America

If an object is constrained to move on the surface of a sphere that is rotating at constant angular velocity, it is well known that within the rotating frame Coriolis and centrifugal accelerations appear. Assuming that there are no physical forces acting on the object that are directed tangentially, one might suppose that the change in velocity of the object over a finite time interval could thus be determined by integrating the sum of the Coriolis and centrifugal accelerations over that time interval. This procedure, however, does not yield the correct value for the velocity change. Owing to performing the calculation in spherical coordinates, additional acceleration contributions must also be included. The constraint forces cannot be the sources of these additional contributions, because the constraints are directed radially, while the additional accelerations are directed tangentially. The required additional acceleration terms are derived from first principles in a manner that would be suitable for presentation in either an undergraduate or graduate mechanics course.