Newton's laws and circular motion
Newton's first law states that an object will continue to move in a straight line with the same velocity if it is not affected by a force. Therefore, an object undergoing circular motion must have a force acting on it that changes its direction.
Newton's second law states that an object under the influence of a force will accelerate in the direction of the force.
This means that the force on the object cannot have components that are in the direction of the velocity. The force must therefore always be perpendicular to the velocity of the object (i.e. pointing to the centre of circular motion).
Acceleration in uniform circular motion is therefore perpendicular to the trajectory. In non-uniform circular motion, a non-zero component remains in the direction of motion.