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

2. First Midterm Exam on Friday
Covers Units 1-3 plus “Math”
One-dimensional Kinematics
Two-Dimensional Kinematics
Relative and Circular Motion
Unit conversion
Trigonometry and Algebra
50 minute duration
Multiple choice
Calculators Allowed/Needed
Three sheets of notes. (equivalent font size>9)(this is font size=9)

3. What type of questions? Interpretation and use of graphs
Which of the following statements about the velocity of the cart is correct?
What is the velocity at t=?
What is the acceleration at t= ? ….

4. What type of questions?
Displacement, velocity and acceleration in 1 dimension
Given some combination of acceleration, initial velocity, final velocity, displacement, elapsed time, etc. calculate an unknown quantity using the kinematic equations….

5. What type of questions?
Motion with constant acceleration in 1-dimension
V0=0m/s
ground
H=10m V1
Given some combination of acceleration, initial velocity, final velocity, displacement, elapsed time, etc. calculate an unknown quantity using the kinematic equations….

6. What type of questions? Relative motion in 2 dimensions
Given some combination of relative velocity between frames of reference answer questions related to the displacement and elapsed times for certain actions…

7. What type of questions? Projectile motion
Given some combination of initial velocity, range , maximum height, etc…calculate characteristics of projectile motion..

8. What type of questions? Circular Motion
Top view
Given some combination of angular velocity, Radius, ac calculate a characteristic of the motion of an object at constant speed in a circle…

9. What type of questions? Any material from Units 1-3 Calculations
Unit conversion
Algebra, trigonometry and vectors
Conceptual Questions
Similar to pre-lecture and checkpoint questions

10. What type of questions? Vectors q
Decompose a vector into polar or Cartesian coordinates
Vector Addition (Subtraction)

11. How to prepare? Read the textbook Review the video prelectures
Review the lecture slides
(Re-)Work homework problems
Prepare three sheets of notes
Basic Fundamental Equations
Derived Equations( and be able to derive them!)
Unit conversions
Algebra notes (quadratic equation)
Trigonometric relations
Vector concepts
Conceptual notes,…
Get enough sleep!!!

12. Main Points of Unit 1

13. Main Points of Unit 1

14. Vectors and 2d-kinematics – Main Points

15. Vectors and 2d-kinematics – Main Points

16. Vectors and 2d-kinematics Important Equations

17. Relative and Circular Motion
a) Relative motion
b) Centripetal acceleration

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

20. Hyperphysics Motion

21. 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

22. Maximum Height of ball thrown upward in gravitational field
What is the velocity of an object when it is at its maximum height?
Two ways to solve for maximum height…
Solve for time first
Solve for position directly
Remember a is negative
Use tf to solve for maximum height…

23. The meeting Problem Whenever possible solve symbolically.
Define your problem; Identify useful equations
Whenever possible solve symbolically.
Then plug in the numbers!!!! You can understand what is going on better if you keep the equations organized.
Start solving…
Gather terms…Does the equation look reasonable?
Solve for desired quantity…
Position of object 1 when object 2 is launched
This time is w.r.t object 2.
To obtain time w.r.t object 1
need to add delay time
Speed of object 1 when object 2 is launched

24. Break problem into parts
Region 1: 0<t<1.5 s
Region 1
Region 2
Region 3
Region 2: 1.5s<t<3.0s
What happened in region 3?
Region 3: 3.0s<t<5.0s
Smartphysics Conclusion

25. 2d-Vectors q
Think of a vector as an arrow. (An object having both magnitude and direction)
The object is the same no matter how we chose to describe it 25

26. Algebra and Trigonometry
Algebra is “fair”
Quadratic Equation
Trigonometry

27. Vector Addition
Add Components!!!
AddTail to Head 27

28. Kinematics in 3D
Note: 3 directions are independent, but share time. 28

29. Projectile Motion
Horizontal
Vertical
Boring 29

30. 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

31. 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)

32. Relative Motion in 2 Dimensions
Speed relative to shore

33. Relative Motion in 2 Dimensions
Direction w.r.t shoreline

34. Centripetal Acceleration
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

35. Additional Slides

36. w is the rate at which the angle q changes:
v = wR
w is the rate at which the angle q changes: q
Once around:
w = Dq / Dt = 2p / T
v = Dx / Dt = 2pR / T

37. v = wR
Another way to see it:
v dt
=R dq dq R
v = Rw

38. Two thrown balls problem #2
Use your equation in symbolic form and gather the values to be used….
Solve for individual elements of equation…can check if things make sense
Position of object 1 at moment object 2 is launched
Velocity of object 1 at moment object 2 is launched
Solve for displacement and relative velocity at time when object 2 launches
Note that acceleration term after 2nd object is released drops out!!!
Divide to obtain time when objects meet

39. Homework Hints – Stadium Wall
Calculate time to reach wall using vx:
Calculate y position at time to reach wall:

40. Homework Hints – Stadium Wall
Calculate time to reach wall using vx:
Calculate y position at time to reach wall:

41. Homework Solutions-Baseball Stadium

42. Plane Ride N E
East of north

43. Car on Curve

44. Maximum Height of Trajectory
Height of trajectory,h=ymax

45. Time of Flight, “Hang Time”

46. Range of trajectory

47. Angle for Maximum Range
MAXIMUM range OCCURS AT 450

48. Height of Trajectory at time t or position x
Height of trajectory, y(t)
Height of trajectory, y(x)

49. Launch Velocity-Given R and 

50. Launch Angle

51. Launch Velocity –Given R and h