1. Circular Motion Circumference:2  r Period = T:definition? Basic quantities in circular motion:

2. Circular Motion Circumference:2  r Period = T:a) time to rotate once b) # of seconds per revolution Basic quantities in circular motion:

3. Circular Motion Period: amplitude angle

4. Circular Motion Period: amplitude angle

5. Circular Motion Period: amplitude angle

6. Circular Motion Period: amplitude angle

7. Circular Motion Period: amplitude angle

8. Circular Motion Period: amplitude angle

9. Circular Motion Period: amplitude angle

10. Circular Motion Period: amplitude angle

11. Circular Motion Period: amplitude angle

12. Circular Motion Period: amplitude angle

13. Circular Motion Period: amplitude angle

14. Circular Motion Period: amplitude angle

15. Circular Motion Period: amplitude angle

16. Circular Motion Period: amplitude angle

17. Circular Motion Period: amplitude angle

18. Circular Motion Period: amplitude angle

19. Circular Motion Period: amplitude angle

20. Circular Motion Period: amplitude angle

21. Circular Motion Circumference:2  r Period = T:a) time to rotate once b) # of seconds per revolution Basic quantities in circular motion: Tangential Velocity:

22. Circular Motion Circumference:2  r Period = T:a) time to rotate once b) # of seconds per revolution Basic quantities in circular motion: Tangential Velocity:

23. Circular Motion Tangential Velocity: Upon what variable in the numerator is the velocity dependent? This is the velocity tangent to the rotating circle, or the linear velocity if the object were released.

24. Circular Motion Tangential Velocity: The radius; the larger the radius the greater the velocity Upon what variable in the numerator is the velocity dependent? This is the velocity tangent to the rotating circle, or the linear velocity if the object were released.

25. Circular Motion Angular Quantities in Physics We designate position on a circle by , the angular position. We use RADIANS.  LinearAngular x 

26. Circular Motion Angular Quantities in Physics  is the change in the angular position. It is called the angular displacement.  LinearAngular x  xx 

27. Circular Motion Angular Quantities in Physics LinearAngular x  xx  It takes time to rotate. If we divide  by time, we get the rate of rotation. 

28. Circular Motion Angular Quantities in Physics LinearAngular x  xx  v  It takes time to rotate. If we divide  by time, we get the rate of rotation.  This is called the angular velocity: 

29. Circular Motion Angular velocity:

30. Circular Motion Angular velocity: Earlier, we defined angular velocity: But what if the rate at which it is spinning changes? We then have:

31. Circular Motion This change in angular velocity takes place over some time interval. Therefore, LinearAngular x  xx  v  a  This quantity is called the angular acceleration, .

32. Circular Motion Note the similarities between angular acceleration and linear acceleration in the format of the equation:

33. Circular Motion We can use our previous analysis in linear kinematics to write the equations for rotational kinematics: 1. 2. 3.

34. Circular Motion Relationship between linear and angular quantities  s r r s = arc length r = radius  = angle in radians

35. Circular Motion Relationship between linear and angular quantities  s r r What is the formula for arc length? s = arc length r = radius  = angle in radians

36. Circular Motion Relationship between linear and angular quantities  s r r

37. Circular Motion Relationship between linear and angular quantities  s r r It takes time to rotate, so divide “s” by time to get the rate of rotation…

38. Circular Motion Relationship between linear and angular quantities  s r r

39. Circular Motion Relationship between linear and angular quantities  s r r tangent velocity angular velocity

40. Circular Motion Relationship between linear and angular quantities  s r r It takes time to increase velocity, so divide “v” by time to get the rate of velocity change…

41. Circular Motion Relationship between linear and angular quantities  s r r

42. Circular Motion Relationship between linear and angular quantities  s r r tangent acceleration angular acceleration