Model for Solving Uniform Circular Motion Problems

(Items in blue are extensions that happen in 2D situations)

(Changes from the Newton's Laws frame are in red)

1.      Sketch the problem indicating all information explicitly or implicitly contained in the problem.  Note, but do not worry about, the apparent goal of your problem solving.

2.      Identify the object or objects of interest and create freebody diagrams for each.  As you do this you will need to define the coordinate axis for your problem along with choosing + and – directions. Label all forces with a coherent system that allows you to distinguish among them. Consider the forces in choosing a coordinate system which maximizes the number of forces which lie along the axes. In the case of circular motion you are strongly advised to choose one of your axes so that it points in the radial direction (towards the center of the circular motion).

  1. If you have more than one object of interest in your problem examine your freebody diagrams for forces which are examples of Newton ’s 3rd Law and therefore equal in magnitude.
  1. If you have any forces which do not lie along one of your axes then you will need to re-express that force by breaking it down into its components along your chosen coordinate system. Following this process redraw your freebody diagram to show all forces and components along your coordinate axes.
  1. If there are objects connected by strings it would be wise to choose coordinate systems for the two objects which are internally consistent in the sense that + motion of one object is also + motion of the associated object.

6.      Write down Newton ’s 2nd Law which describes the net forces acting along the axes you have chosen. I would encourage you to first write it in vector form where the net force is the vector sum of all the forces along your axis. Keep the forces on one side of the equation and the effects (the acceleration) on the other.

In the case of circular motion you know that the acceleration in the radial direction is given by v2/r (or rω2). This is the result of the collective effect of the forces you have identified on your freebody diagram. There is no new force(s) added to the problem because the object moves in a circle. Be sure that you can clearly identify the source of each force on your freebody diagram and don't make any desperate appeals other mysterious forces you may have heard about.

7.      Rewrite Newton ’s 2nd Law in “scalar” form where the direction of each force is assigned by considering your choice of coordinate system. At this time consider whether you have enough information to solve the equations or do you need to seek additional information by returning to step 6 and considering another object’s contribution to the problem.

  1. In the event that friction plays a role in the problem you will need to consider several things. First you will need to decide whether it is static or kinetic friction and what to do about that pesky inequality if static friction is what’s happening. Then you will probably want include in your list of useful equations the standard physics friction model.

9.      If your equations are now solvable then proceed with the algebra until you have a solution for your target quantity. Then plug in the numbers, WITH UNITS, and calculate a numerical solution.

10.  Consider your answer and whether it makes sense. Use the various tools we have discussed to ascertain whether your solution is reasonable.