I've been thinking about centripetal force and its effects on motion in uniform circular motion. I've actually found it difficult to accept that velocity magnitude can ever be maintained constant. Here is why: if this is our velocity vector, v, at the top of the circle: → Then the centripetal acceleration vector must then point downward (perpendicular to the velocity vector. However, acceleration that is perpendicular to a component has no effect on that component. In other words, if you have acceleration in the y axis, this has no effect on velocity on the x axis. So here is my question: how is it possible that centripetal acceleration can change the direction of the velocity at the top of the circle without affecting its magnitude? After all, the x component of the above vector, v (→) is the only component of said vector. If acceleration is point perpendicular to this vector, how, then, can the next vector for velocity (which would point slightly diagonal) have the same magnitude as the original vector v? Would it not have an x component whose magnitude would be equivalent to that of vector v PLUS a y component, thus summing up to a larger magnitude?