Uniform circular motion (UCM) describes the motion of an object moving at a constant speed in a circular path. Centripetal force is directed towards the center of curvature and causes the object to travel in a circular path. During UCM, centripetal force and centripetal acceleration are directed towards the center, while the velocity is tangential to the path. Examples show that the centripetal force can be the force of friction, normal force, tension, or gravity depending on the situation.

1. Uniform Circular Motion

2. UCM is the motion of an object along a circular path at a constant speed

3. Centripetal force is any force or sum of forces that cause an object to move in UCM

4. During UCM centripetal force and centripetal acceleration are directed towards the center of the curvature

5. The velocity of the object is directed away from the curvature/tangential to the curvature

6. Example Problems

8. This is because Normal and Gravity cancel out because they are equal.

9. So in this case So F c =F f

11. This is because gravity is cancelled out by the force of friction

12. In this case F c =F N

14. This is because gravity is cancelled out by the force of normal

15. In this case F c =F t

17. This is because there is no other force acting on the planet

18. So in this case F c =F g /mg

19. Steps for Solving a UCM Problem

20. Decide which formula to use- Fc=mAc or Ac=v^2/r

21. Plug the variables in, and in the case of Fc, plug the ac formula into the Fc one.