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Uniform Circular Motion (UCM) same along a circular path Uniform Circular Motion -- motion around a circular path at a constant speed. 1 Conditions describing UCM: v • speed = const. (by definition) • v ≠ const. (since direction is changing) ⇒ a≠o Fnet ≠ 0 2 During UCM the sum of all the forces acting on the object (Fnet) ≠ 0 and the object is accelerating. 3 In case of UCM the vectors for acceleration and force point toward the center. v 4 Centripetal Force -- any force that makes an object move in UCM. Examples: 1. As the car curves a turn, a passenger is thrown against the window. What is the force making the passenger's trajectory curve? 5 2. An object attached to a rope and moving in a circular path (see picture) 3. A car moving in a circular path 6 4. Moon orbiting Earth (assuming UCM) 5. An amusement park ride which consists of a large cylinder on radius R spinning about its vertically oriented axis of symmetry. When the ride reaching a specific speed, the floor drops and people remain "fixed" to the walls of the ride. 7 6. Rollecoaster (* not a true UCM) 8 Formulas Describing UCM Speed during UCM r Radius of the circle r and time t it takes the car to complete 1 full circle are known. This time is called a period of rotation (T) Find speed. 9 In the reference table find the formula for centripetal acceleration ac = v2/r where ac -- centripetal acceleration v -- speed r -- radius 10 In the reference table find the formula for centripetal force Fc = mac where Fc -- centripetal force m -- mass ac -- centripetal acceleration 11 Captain Chip, the pilot of a 60,500 kg plane, is told that he must remain in a holding pattern over the airport until it is his turn to land. (a) What is the nature of centripetal force acting on the plane? (b) If Captain Chip flies his plane in a circle whose radius is 50.0 km once every 30.0 min, what is the size of the centripetal force? 12 13 Missy's favorite ride at the amusement park is a ride called "Rotor". The Rotor has a radius of 4.0 m and it takes a ride 2.0 sec to complete one full revolution. (a) What is Missy's linear/tangential speed on the Rotor? (b) What is Missy's centripetal acceleration on the Rotor? (c) If Missy's mass is 55 kg, what is the value of the normal force acting on her? (d) If the coefficient of friction between Missy and the wall is 0.65, find the magnitude of the force of friction. (e) Is the frictional force large enough to keep Missy "glued" to the wall of the Rotor? 14 15 16 17