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Centripetal Acceleration
Whenever a net force acts perpendicular to the motion (velocity) of the object, the object's magnitude of velocity will not change but the direction will. That is exactly what happens when an object is undergoing uniform circular motion. The net force, and hence the acceleration point directly towards the center of the circle circumscribed by the pathway of the object. However, at any given point the velocity vector is tangent to the circle at that point. Therefore, whenever an object is undergoing uniform circular motion, the centripetal acceleration is exactly perpendicular to the velocity of the object. As it turns out, even though the magnitude of velocity (speed) remains constant, the object's velocity is still changing because the direction of the vector changes. In fact, we can derive the formula for centripetal acceleration (also called radial acceleration) as shown in lecture. We see that the radial acceleration is found by squaring the velocity and dividing the result by the radius of the circle.
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