Centripetal and Centrifugal Forces Chapter 10.3-10.5 Notes

Centripetal Force Remember that an object’s velocity requires both a speed and direction Acceleration is the change in velocity divided by time; even if an object is moving at a constant speed, it is accelerating if it changes direction Any object that is traveling in a circle undergoes acceleration that is directed at the center of the circle—called centripetal acceleration Centripetal means “toward the center” The centripetal force is the force directed toward a fixed center that causes an object to follow a circular path

Examples of Centripetal Forces The centripetal force on an object depends on an object’s tangential speed, its mass, and the radius of its circular path Imagine if you whirl a tin can on the end of a string—you have to pull on the string, which exerts a centripetal force The string transmits the centripetal force, pulling the can from a straight-line path into a circular path

Examples of Centripetal Forces If a car is traveling in a curved path, there must be enough friction to provide the required centripetal force If there is not enough friction, the car will skid

Calculating Centripetal Forces Greater speed and greater mass require a greater centripetal force Also, traveling in a circular path with a smaller radius of curvature requires a greater centripetal force Centripetal force, Fc, is measured in newtons when m is measured in kilograms, v in meters/second, and r in meters

Adding Force Vectors A conical pendulum is a bob held in a circular path by a string attached above it The string sweeps out in the shape of a cone The only two forces that act on the bob is the force due to gravity (its weight), mg, and the tension in the string, T Both are vectors

Components of the Tension Vector The vector T can be resolved into two perpendicular components, Tx (horizontal), and Ty (vertical) Since the bob doesn’t accelerate vertically, the net force in the vertical direction is zero Therefore, Ty must be equal and opposite to mg Tx is the net force on the bob—the centripetal force. It is equal to mv/r2, where r is the radius of the circular path

Centrifugal Forces So far, we have only discussed circular motion as being caused by a center-directed force Sometimes an outward force on a rotation or revolving body is called a centrifugal force Centrifugal means “center-fleeing,” or “away from the center” It is a common misconception that the centrifugal force pulls outward on an object

Centrifugal Forces Example: suppose you are the passenger in a car that suddenly stops. If you’re not wearing a seat belt, you will bend forward toward the dashboard. The reason is not because something forced you forward; rather, it is because of the absence of a force—the seat belt wasn’t holding you back Similarly, if you’re in a car that rounds a sharp corner to the left, you lean to the right. There was not a force that pulled you outwards toward the right, but rather there is no centripetal force holding you in circular motion

Centrifugal-force effect The centrifugal force is not due to any real force Rather, the “centrifugal-force effect,” or the belief that a force is pulling outwards on an object that is in circular motion, is really just due to inertia If objects are not held in circular motion due to the centripetal force, they will just continue to move in a straight-line path The centrifugal force is an effect of rotation—it is not part of an interaction and therefore it cannot be a true force. Physicists refer to the centrifugal force as a fictitious force