The Algorithm

  1. Determine if the system is in UCM
  2. If it is orient axis so one direction points radially inward.
  3. Determine if the other direction should be tangential to the circle or one of the traditional X or Y directions.
  4. Follow the procedure for Newton's 2nd Law
  5. Equate the radial acceleration with v2/r
 

Other Resources

A pretty good video showing how to solve UCM problems with insights into why certain assumptions/conclusions are made. Beware, there are no vector symbols and the units are "sloppy."