1. Circular Motion AP Physics C Mrs. Coyle

2. Circular Motion Uniform circular motion (constant centripetal acceleration) Motion with a tangential and radial (centripetal)acceleration

3. Uniform Circular Motion Object has a circular path, constant speed. The velocity is always tangent to the path of the object.

4. Why is there acceleration in uniform circular motion? v = v f – v i a= v/t

5. Centripetal Acceleration Vector Always perpendicular to the path of the motion. Points toward the center of the circle.

6. Characteristics of UniformCircular Motion Tangential (linear) Velocity Frequency Period Centripetal Acceleration

7. Frequency, f : #revolutions per unit time f = # rev / time Units: (1/sec)=sec -1 =Hertz (Hz) rpm (#rev/min) rps (#rev/sec) r

8. Period Period T : time for 1 revolution –Unit: sec, min, h Relating Frequency and period f= 1 T

9. Tangential Speed in terms of T or f v=2r/T v=2rf

10. 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/s 2

11. Tangential Acceleration When v varies. Motion is not uniform circular motion.

12. Total Acceleration Tangential acceleration (vector) Plus Radial acceleration (vector)

13. Tangential acceleration: Radial acceleration: Total acceleration: Total Acceleration

14. –r, radius vector , tangent to the circle

15. Example 2 (#34) An automobile whose speed is increasing at a rate of 0.6m/s 2 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 magnitude and direction of the total acceleration. Ans: a)0.6m/s 2,b)0.8m/s 2, c)1m/s 2,53.1 o