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Circular Motion AP Physics C Mrs. Coyle Circular Motion Uniform circular motion (constant centripetal acceleration) Motion with a tangential and radial (centripetal)acceleration Uniform Circular Motion Object has a circular path, constant speed. The velocity is always tangent to the path of the object. Why is there acceleration in uniform circular motion? Dv = vf vi a= Dv/ Dt Centripetal Acceleration Vector Always perpendicular to the path of the motion. Points toward the center of the circle. Characteristics of UniformCircular Motion Tangential (linear) Velocity Frequency Period Centripetal Acceleration Frequency, f : #revolutions per unit time f = # rev / time Units: (1/sec)=sec-1=Hertz (Hz) rpm (#rev/min) rps (#rev/sec) r Period Period T : time for 1 revolution Unit: sec, min, h Relating Frequency and period f= 1 T Tangential Speed in terms of T or f v=2pr/T v=2prf Example 1 A boy whirls a stone in a horizontal circle of r=1.5m, 2m above the ground. The string breaks and the stone strikes 10m away. What was the centripetal acceleration during the circular motion? Answer: 160m/s2 Tangential Acceleration When v varies. Motion is not uniform circular motion. Total Acceleration Tangential acceleration (vector) Plus Radial acceleration (vector) Tangential acceleration: Radial acceleration: Total acceleration: Total Acceleration Total Acceleration r, radius vector - q , tangent to the circle Example 2 (#34) An automobile whose speed is increasing at a rate of 0.6m/s2 travels on a circular road of radius 20m. When the instantaneous speed of the car is 4m/s find: a)the tangential acceleration, b)the centripetal acceleration, c)the mag