Aim: How do we explain centripetal motion?

Uniform Circular Motion An object that moves in a circle at constant speed is said to undergo uniform circular motion (centripetal motion).

Uniform Circular Motion How do we know that the object (blue particle) is accelerating? IT CHANGES DIRECTION What is the direction of the object’s acceleration? TO THE CENTER OF THE CIRCLE What is the direction of the object’s instantaneous velocity? TANGENT TO THE CIRCLE

Uniform Circular Motion The centripetal acceleration of an object is always directed toward the center. The instantaneous velocity of an object in centripetal motion is always directed tangent to the circular path.

Equation for Centripetal Acceleration and centripetal force Centripetal Acceleration = ac Speed = v Radius of circular path = r ac = v2/r

Centripetal Force When an object is in uniform circular motion, the net force acting on the object is called the centripetal force. Fnet=Fc=mac=mv2/r The centripetal force can be equal to a single force or the sum of a combination of forces. The centripetal force always has the same direction as the centripetal acceleration.

Centripetal vs centrifugal When the subject of circular motion is discussed, it is not uncommon to hear mention of the word centrifugal. Centrifugal, not to be confused with centripetal, means away from the center or outward. The use of or at least the familiarity with this word centrifugal, combined with the common sensation of an outward lean when experiencing circular motion, often creates or reinforces a common student misconception. The common misconception, believed by many physics students, is the notion that objects in circular motion are experiencing an outward force. "After all," a well-meaning student may think, "I can recall vividly the sensation of being thrown outward away from the center of the circle on that roller coaster ride. Therefore, circular motion must be characterized by an outward force." This misconception is often fervently adhered to despite the clear presentation by a textbook or teacher of an inward force requirement. As discussed previously in Lesson 1, the motion of an object in a circle requires that there be an inward net force - the centripetal force requirement. There is an inward-directed acceleration that demands an inward force. Without this inward force, an object would maintain a straight-line motion tangent to the perimeter of the circle. Without this inward or centripetal force, circular motion would be impossible.

Thought question 1 You are riding on a Ferris wheel that is rotating with constant speed. The car in which you ride always maintains its correct upward orientation-it does not invert. What is the direction of your centripetal acceleration when you are (a) at the top of the wheel? (b) At the bottom of the wheel? What is the direction of the normal force on you from the seat when you are (c) at the top of the wheel? (d) At the bottom of the wheel? (e) At which point, top or bottom, is the normal force largest in magnitude? a) Downward b) upward c) upward d) upward e) bottom

Thought Question 1

ThoughT question 2 A car travels on a circular roadway of radius r. The roadway is flat. The car travels at a high speed v, such that the friction force causing the centripetal acceleration is the maximum possible value. If this same car is now driven on another flat circular roadway of radius 2r, and the coefficient of friction between the tires and the roadway is the same on the first roadway, what is the maximum speed of the car such that it does not slide off the roadway? √2v

Thought Question 3 High-speed curved roadways are banked-that is, the roadway is tilted toward the inside of tight curves. Why is this? The normal force is able to add to the centripetal force (in addition to the static friction force). Instead of just friction supplying the centripetal force, when the road is banked, there is a component of the normal force which also supplies the centripetal force. Thus the maximum speed that a car can travel at around the roadway increases

Thought question 2

Thought question 3