1. Comprehensive Review Comprehensive Review a) Exam information
b) What kind of questions?
c) Review

2. Midterm 3 Exam in-class
Average = 5.1/12
Average = 57% (normalized to 9)
The score for Midterm 3 will be calculated with the following formula:

3. Final Exam Review the following material
homework problems.
video pre-lectures/textbook.
Lecture slides
Unit Main Points
Multiple choice…but show your work and justification.
Mostly Calculations…”step by step”
Some Conceptual questions…like checkpoint problems.
Bring calculators and up to ten sheets of notes.
It is best to prepare your own hand-written notes!
Derived Equations may be helpful…(e.g. projectile motion)

4. Kinematics Force Energy Conservation Laws Collisions Rotations
What we covered…
Kinematics
Description of Motion
Force
Dynamics-how objects change velocity
Energy
Kinetic and Potential
Conservation Laws
Momentum and Energy
Collisions
Elastic and In-elastic
Rotations
Torque/ Angular Momentum/Statics

5. Problem Solving Techniques
Visualize/Diagram
“Sketch” problem
Identify variables, input and what we are trying to solve
Free-body diagrams
Express in Mathematical Equations
Scalars-1d
Vectors-2d,3d Break into components
System of n-equations with n-unknowns
Use Mathematical tools to solve:
Quadratic Equation
Vector operations
Trigonometry
Conceptual Understanding
Does answer make sense?

6. Potential Problem Topics
Projectile Motion
Relative Motion - 2d
Uniform Circular Motion
Forces
Weight (near earth)
Gravitational (satellite)
Springs
Normal Force
Tension
Friction
Free-Body Diagrams
Work-Kinetic Energy
Potential Energy
Center of Mass
Conservation of Momentum
Collisions
In-elastic
Elastic
Rotations
Kinematics
Dynamics
Statics
Moment of Inertia
Torque
Angular Momentum

7. Relevant Formulae

8. Relevant Formulae

9. Kinematics

10. Hyperphysics Motion
Displacement vs timet
Velocity vs timet
Acceleration vs timet

11. Hyperphysics Motion

12. 1d-Kinematic Equations for constant acceleration
Basic Equations to be used for 1d – kinematic problems.
Need to apply to each object separately sometimes with time offset
When acceleration changes from one constant value to another say a=0 The problem needs to be broken down into segments

13. Ballistic Projectile Motion Quantities
Initial velocity
speed,angle
Maximum Height of trajectory, h=ymax
“Hang Time”
Time of Flight, tf
Range of trajectory, D
Height of trajectory at arbitrary x,t

14. Derived Projectile Trajectory Equations
Maximum height
Time of Flight (“Hang Time”)
Range of trajectory
Height of trajectory as f(t) , y(t)
Height of trajectory as f(x), y(x)

15. Relative Motion in 2 Dimensions
Direction w.r.t shoreline
Speed relative to shore

16. Uniform Circular Motion

17. Uniform Circular Motion
Constant speed in circular path
Acceleration directed toward center of circle
What is the magnitude of acceleration?
Proportional to:
Speed
time rate of change of angle or angular velocity
v = wR

18. Dynamics

19. Inventory of Forces Weight Normal Force Tension Gravitational Springs
…Friction

22. m2
1) FBD N T m2 g f T m1 m1
m2g
m1g 22

23. m2 N T m2 f T m1 m2g N = m2g m1g m1g – T = m1a T – m m2g = m2a
1) FBD
2) SF=ma N T m2 g f T m1 m1
m2g
N = m2g
m1g
T – m m2g = m2a
m1g – T = m1a
add
m1g – m m2g = m1a + m2a
m1g – m m2g
a =
m1 + m2 23

24. m2 N T m2 f T m1 m2g m1g m1g – T = m1a T = m1g – m1a 1) FBD 2) SF=ma g
m1g – m m2g
T = m1g – m1a
a =
m1 + m2
T is smaller when a is bigger 24

25. Gravitation Problems…too!

26. Be careful what value you use for r
Be careful what value you use for r !!! Should be distance between centers of mass of the two objects

27. Work-Kinetic Energy Theorem
The work done by force F as it acts on an object that moves between positions r1 and r2 is equal to the change in the object’s kinetic energy:
But again…!!!

28. Energy Conservation Problems in general
For systems with only conservative forces acting
Emechanical is a constant

29. (otherwise objects velocity is constant)
Determining Motion
Force
Unbalanced Forces  acceleration
(otherwise objects velocity is constant)
Determine Net Force acting on object
Use kinematic equations to determine resulting motion
Energy
Total Energy  Motion, Location
Work
Conservative forces
Motion from Energy conservation

30. Friction
“It is what it has to be.”

31. Block

32. Work & Kinetic Energy

33. Example Problem

34. Potential Energy

35. Example Problems

36. Example: Pendulum h h
Conserve Energy from initial to final position.

37. Gravitational Potential Problems
conservation of mechanical energy can be used to “easily” solve problems.
Define coordinates: where is U=0?
Add potential energy from each source. as

38. Collisions Center of Mass Conservation of Momentum
Inelastic collisions
Elastic Collisions
Impulse and Reference Frames
Multiple particles, Solid Objects
Isolated system, No external force
Non-conservative internal force
Conservative internal force
Individual Particle changes momentum due to Force acting over a given duration
Favg = DP/Dt

39. Systems of Particles

40. Example Problem

41. Collisions

42. Example Problem

43. Example Problem :

44. Impulse

45. |Favg | = |DP | /Dt = 2mv cosq /Dt

46. Rotations Rotational Kinematics Moment of Inertia Torque
Rotational Dynamics
Rotational Statics
Angular Momentum
Description of motion about a center of mass
Resistance to changes in angular velocity
Force applied at a lever arm resulting in angular acceleration
Newton’s 2nd law for rotations
How to ensure stability
Vector Quantity describing object(s) rotation about an axis

47. Rotational Kinematics

48. Rotational Dynamics

49. Example Problem

50. Example Problem

51. Work & Energy (rotations)

52. Example Problem

53. Statics

54. Statics Problems

55. Example Problem

56. Angular Momentum

57. Example Problem

58. Relevant Formulae

59. Relevant Formulae