I've got a question about circular motion that's been bugging me for a while.
Suppose we have a ball in circular motion. At a certain point in time, the ball experiences a centripetal force that is perpendicular to its velocity.
By right, the centripetal force should cause the velocity of the ball to increase (accelerate) perpendicular to its initial velocity. Then, the two velocities combine and we get a third velocity with a larger magnitude than the initial velocity and points in a new direction. Basically, like a ball in projectile motion.
But obviously, this isn't the case because the magnitude of velocity (speed) of the ball stays constant, only the direction changes. So something is obviously wrong with my reasoning.