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Circular Motion Notes Uniform Circular Motion – is the movement of an object at constant speed around a circle with a fixed radius. Centripetal Acceleration – The acceleration of an object in uniform circular motion. The centripetal acceleration always points towards the center. ac = v2/ r Where ac = centripetal acceleration v = tangential velocity r = radius Centripetal Force – The net force acting toward the center of a circle to keep an object moving in a circular path. Fc = mac or Fc = mv2/ r Where m = mass ac = centripetal acceleration r = radius v = tangential velocity Critical velocity – The minimum velocity required for a satellite to travel a circular path of radius r. vc = (rg) Where r = radius (m) g –acceleration due to gravity Critical velocity – The maximum speed a car can safely round a curve. vc = (rg) Where: r = radius = coefficient of friction g –acceleration due to gravity The number of g’s an object experiences. #g’s = acceleration/ 9.8 Circumference of a circle: c = 2r Period of a pendulum: The time for a pendulum to make one complete oscillation. T = 2(L/g) Where: T = Period of a pendulum (s) L = Length of a Pendulum (m) g –acceleration due to gravity (m/s2) Example1. It takes a 615 kg racing car 14.3 seconds to travel at a uniform speed around a circular racetrack of 50.0 meters radius. a. What is the acceleration of the car? b. What average force must the track exert on the tires to produce this acceleration? Example 2. An athlete whirls a 7.00 kg hammer tied to the end of a 1.3 m chain in a horizontal circle. The hammer moves at the rate of 1.0 rev/s. a. What is the centripetal acceleration of the hammer? b. What is the tension in the chain? Example 3. A teacher is twirling his keys (m = 100g) in a vertical circle attached to a key chain 5cm long. If the tension in the bottom of the chain is 4N, what is its uniform speed? What is the tension at the top of the chain? Example 4. A ball at the end of an 80 cm string is being whirled in a vertical circle. At what minimum velocity will the string begin to go slack at the top of the ball’s path? Example 5. The coefficient of static friction between a car’s tire and a certain concrete road is 1.0 when the road is dry and 0.7 when the road is wet. If the car can safely make the turn at 25 mi/h on a dry day, what is the maximum velocity on a rainy day? Example 6. What is the length of a pendulum having a period of 3 seconds where gravity is 9.8 m/s2 Example 7. A pendulum 110 cm long has a period of 2.1 seconds. If the value of gravity is decreased by 75%, what would be the period?