Uniform Circular Motion

• Uniform Circular Motion (UCM) occurs when an object moves with a constant speed around a circular path.
• The speed remains constant, but the velocity does not because the object's direction is always changing. The object must accelerate towards the center of the circle to stay in the circular path.
• The magnitude of this centripetal acceleration is

                            v^2 
                     a  =  -----
                             r
  

  where v is the speed of the object and r the radius of its circular path.
• As Newton's First Law states, objects do not accelerate unless they are acted upon by a force. In order to maintain an object in UCM, one must exert a centripetal force of magnitude

                                          v^2 
                     F  =  m * a  =  m * -----
                                           r
  

  and in the direction of the center of the circle.