2. Department of Physics and Astronomy
PHY/EGR
Spring 2008
Harry D. Downing
Professor and Chair
Department of Physics and Astronomy

3. Roll Call Fill out Student Information Sheets
Pass out syllabi then go to next slide
Take pictures of each student in lab today

4. Let’s visit the web for course information.
Downing’s PHY/EGR 321 Home Page
physics.sfasu.edu

5. Homework Format

6. Cover Page
Staple at 450
NAME
PHY/EGR
Date
Problems
Grade

7. Cover Page, Example Pass out some example engineering pad paper
Staple at 450
Harry Downing
PHY/EGR
Ch 11 – 2, 6, 9, 16
Grade 5, 4, 5, 3
Pass out some example
engineering pad paper

8. Kinematics of Particles
CHAPTER 11
Kinematics of Particles

9. 11.1 INTRODUCTION TO DYNAMICS
Galileo and Newton (Galileo’s experiments led to Newton’s laws)
Kinematics – study of motion
Kinetics – the study of what causes changes in motion
Dynamics is composed of kinematics and kinetics

10. RECTILINEAR MOTION OF PARTICLES

11. 11.2 POSITION, VELOCITY, AND ACCELERATION
For linear motion x marks the position of an object. Position units would be m, ft, etc.
Average velocity is
Velocity units would be in m/s, ft/s, etc.
The instantaneous velocity is

12. The average acceleration is
The units of acceleration would be m/s2, ft/s2, etc.
The instantaneous acceleration is

13. Notice
If v is a function of x, then
One more derivative

14. Consider the function Plotted x(m) t(s) v(m/s) t(s) a(m/s2) t(s) 16 3216 32
t(s) 2 4 6
v(m/s) 12
-12
-24
-36 2 4 6
t(s)
a(m/s2) 12
-12
-24 2 4 6
t(s)

15. 11.3 DETERMINATION OF THE MOTION OF A PARTICLE
Three common classes of motion

19. with
then get

20. or
Both can lead to

21. Work Some Example Problems

22. 11.4 UNIFORM RECTILINEAR MOTION

23. 11.5 UNIFORMLY ACCELERATED RECTILINEAR MOTION
Also

24. 11.6 MOTION OF SEVERAL PARTICLES
When independent particles move along the same line,
independent equations exist for each.
Then one should use the same origin and time.

25. Relative motion of two particles.
The relative position of B with respect to A
The relative velocity of B with respect to A

26. The relative acceleration of B with respect to A

27. Let’s look at some dependent motions.

28. xA G xB C D A B E F
Let’s look at the relationships.
System has one degree of freedom since only one coordinate can be chosen independently.

29. xC xA xB C A B System has 2 degrees of freedom.
Let’s look at the relationships.

30. Work Some Example Problems

31. 11.7 GRAPHICAL SOLUTIONS OF RECTILINEAR-MOTION
Skip this section.

32. 11.8 OTHER GRAPHICAL METHODS
Skip this section.

33. CURVILINEAR MOTION OF PARTICLES
11.9 POSITION VECTOR, VELOCITY, AND ACCELERATION x z y P’ P
Let’s find the instantaneous velocity.

34. x z y x z y P’ P

35. x z y x z y x z y P’
Note that the acceleration is not
necessarily along the direction of
the velocity. P

36. 11.10 DERIVATIVES OF VECTOR FUNCTIONS

38. Rate of Change of a Vector
The rate of change of a vector is the same with respect to a fixed frame and with respect to a frame in translation.

39. 11.11 RECTANGULAR COMPONENTS OF VELOCITY AND ACCELERATION

40. y x z y P x z

41. x z y

42. Velocity Components in Projectile Motion

43. 11.12 MOTION RELATIVE TO A FRAME IN TRANSLATIONx’ z’ y’ B x z y A O

46. Work Some Example Problems

47. 11.13 TANGENTIAL AND NORMAL COMPONENTS
Velocity is tangent to the path of a particle.
Acceleration is not necessarily in the same direction.
It is often convenient to express the acceleration in terms of components tangent and normal to the path of the particle.

48. Plane Motion of a Particlex y P’ P

51. O x y P’ P

52. Discuss changing radius of curvature for highway curves

53. Motion of a Particle in Spacex y P’ P z
The equations are the same.

54. 11.14 RADIAL AND TRANSVERSE COMPONENTS
Plane Motion x y P

57. x y

59. Extension to the Motion of a Particle in Space:
Cylindrical Coordinates

60. Work Some Example Problems