When a particle travels in a circle of radius r, at constant speed v, what is its acceleration

v²/r, towards the center of the circle.Remember that acceleration is the rate of change of velocity, not merely of speed. This means that the change in direction is important. In a unit of time, the velocity vector will rotate by a small angle. This angle is proportional to the angular velocity (w) and to the size of the time unit. This means that the acceleration has magnitude vw. Since w=v/r, this is v²/r. Since the speed is constant, we know that the force is acting perpendicular to the direction of motion, so we finally have v²/r towards the center of the circle.