Recall the interesting type of acceleration associated with circular motion. An acceleration which does not change the speed of a body but which does change the direction of the velocity vector. This type of acceleration is no less real than acceleration which changes velocity and according to Newton's second law it requires a force.
The mistake that is typically made here is to say that because a body is in circular motion it is subject to a ``centripetal force'' along with the gravitational force and perhaps the force associated with tension in a string. This is wrong! The centripetal force is not a new type of force.
To make the argument right I compare to a more familiar situation. What I wish to show is how observation of motion can lead to a conclusion about the net force acting on the body. One example comes from looking at an object lying still on a table, say. Because there is no acceleration we conclude that there is no net force acting on the brick. Slightly more complicated is the case of observing an object moving with constant acceleration. If we measure position versus time and find a parabolic x(t) curve then we can conclude that we have motion with constant acceleration and we can determine the magnitude and direction of acceleration. This observation of kinematics leads to the conclusion that the net force acting on the object is F=ma.
Thus a study of the motion of a body can lead to a conclusion about the
net force acting on that body. This is no different in the case
of uniform circular motion or any more complicated type of motion for
that sake. If I observe a body in uniform circular motion I can
conclude that the net force acting on that body is
Again this is no new force. Just a conclusion about the net force
derived by combining results from kinematics with
Newton's second law.
We shall look at two examples in which we analyze the forces involved in objects which move in uniform circular motion.