We say an object experienced uniform circular motion iff it moves in a circle of constant radius, with constant angular velocity.
To experience uniform circular motion, must the net force on the object be directed towards the center of the circle? For example, a person in a graviton ride experiences the normal force on his back, which is directed towards the center of the graviton, and also the static friction force which allows his seat to move him in a circle. These forces are perpendicular, with the normal force acting radially and the static friction force acting tangentially. But the person still meets all the criteria for uniform circular motion, right?
Secondly, if an object undergoes uniform circular motion, what can be said about the centripetal force? Is the centripetal force equal to the net force on the object, or is it equal to the net force in the radial direction. I believe it is the latter, since if we are to calculate the centripetal force on the person in the graviton, we should not need to worry about the tangential static friction force. But, according to the derivation of the acceleration of a body undergoing circular motion found here the net acceleration, and hence the net force, acts radially.
Thirdly, if the motion is non-uniform, can we say that the net radial force is equal to the standard centripetal acceleration, $v^2/r$?