1. Chapter 3 Outline Motion in Two or Three Dimensions Position and velocity vectors Acceleration vectors Parallel and perpendicular components Projectile motion Uniform circular motion Relative velocity

2. Position Vector

3. Velocity Vector

5. Acceleration Vector

7. Parallel and Perpendicular Components of Acceleration

8. Projectile Motion Any body that is given an initial velocity and follows a path determined solely by the effects of gravity and air resistance is a projectile. The path the projectile follows is its trajectory. Initially, we will consider the simplest model in which we neglect the effects of air resistance, and the curvature of the earth.

9. Projectile Motion

12. Trajectory Shape

13. Projectile Motion Example #1

14. Projectile Motion Example #2

15. Projectile Motion Exam Question Example

16. Circular Motion Changes in direction mean changes in velocity. Special case: Uniform circular motion Constant speed No tangential acceleration, only perpendicular

17. Uniform Circular Motion

18. Nonuniform Circular Motion

19. Circular Motion Example

20. Relative Velocity When you are driving, and pass a car, it appears to be moving backwards. Relative to the ground, it is still moving forward. Relative to you, a moving frame of reference, it is moving backwards. What is the actual velocity? Any frame that is moving at a constant velocity is equally valid. This, along with the constant speed of light, is the basis of special relativity. Generally, if we do not explicitly state a frame, we measure relative to the ground.

21. Relative Position in One Dimension

22. Relative Velocity in One Dimension

23. Relative Velocity in Two or Three Dimensions

24. Relative Motion Example

25. Chapter 3 Summary Motion in Two or Three Dimensions

27. Chapter 4 Outline Newton’s Laws of Motion Forces Contact and long range Superposition Newton’s first law Inertial frames of reference Newton’s second law Mass vs. weight Newton’s third law Inertial frames of reference Free-body diagrams

28. Forces Forces are interactions between two bodies or between a body and the environment. Contact force Push, pull, friction… Long-range Gravitational, electric, magnetic… Vectors!

29. Superposition of Forces

30. Newton’s First Law Natural state of an object Aristotle, Galileo, Descartes… From Pricipia, the Latin followed by an English translation. “Lex I: Corpus omne perseverare in statu suo quiescendi vel movendi uniformiter in directum, nisi quatenus a viribus impressis cogitur statum illum mutare.” “Law I: Every body persists in its state of being at rest or of moving uniformly straight forward, except insofar as it is compelled to change its state by force impressed.” From out text: A body acted on by no net force moves with constant velocity (which may be zero) and zero acceleration.