1. Physics Beyond 2000
Chapter 1
Kinematics

2. Physical Quantities
Fundamental quantities
Derived quantities

3. Fundamental Quantities
Quantity
Symbol
SI Unit
Mass m kg
Length l
Time t s
Others -

4. Derived Quantities Can be expressed in terms of the basic quantities
Examples
Velocity
Example 1
Any suggestions?

5. Derived Quantities
More examples

6. Standard Prefixes Use prefixes for large and small numbers Table 1-3
Commonly used prefixes
giga, mega, kilo
centi, milli, micro, nana, pico

7. Significant Figures
The number of digits between the Most significant figure and least significant figure inclusive.
The leftmost non-zero digit is the most significant figure.
If there is no decimal point, the rightmost non-zero digit will be the least significant figure.
If there is a decimal point, the rightmost digit is always the least significant figure.

8. Scientific Notation
Can indicate the number of significant numbers

9. Significant Figures
Examples 5 and 6.
See if you understand them.

10. Significant Figures Multiplication or division.
The least number of significant figures.
Addition or subtraction.
The smallest number of significant digits on the right side of the decimal point.

11. Order of Magnitude
Table 1-4.

12. Measurement Practice Length Meter rule Vernier caliper
Micrometer screw gauge
Practice

13. Measurement
Time interval
Stop watch
Ticker tape timer
Timer scaler

14. Measurement
Mass
Triple beam balance
Electronic balance

15. Measurement
Computer data logging

16. Error Treatment Personal errors Random errors System errors
Personal bias
Random errors
Poor sensitivity of the apparatus
System errors
Measuring instruments
Techniques

17. Accuracy and Precision
How close the measurement to the true value
Precision
Agreement among repeated measurements
Largest probable error tells the precision of the measurement

18. Accuracy and Precision
Examples 9 and 10

19. Accuracy and Precision
Sum and difference
The largest probable error is the sum of the probable errors of all the quantities.
Example 11

20. Accuracy and Precision
Product, quotient and power
Derivatives needed

21. Kinematics
Distance d
Displacement s

22. Average Velocity
Average velocity
= displacement  time taken

23. Instantaneous Velocity
Rate of change of displacement in a very short time interval.

24. Uniform Velocity
Average velocity = Instantaneous velocity when the velocity is uniform.

25. Speed
Average speed
Instantaneous speed

26. Speed and Velocity
Example 13

27. Relative Velocity The velocity of A relative to B
The velocity of B relative to A

28. Relative Velocity
Example 14

29. Acceleration
Average acceleration
Instantaneous acceleration

30. Average acceleration Example 15 Average acceleration =
change in velocity  time
Example 15

31. Instantaneous acceleration
Example 16

32. Velocity-time graph v-t graph
Slope: = acceleration

33. v-t graph
Uniform velocity: slope = 0 v t

34. v-t graph
Uniform acceleration: slope = constant v t

35. Falling in viscous liquid
Acceleration
Uniform velocity

36. Falling in viscous liquid
uniform speed:
slope = 0
acceleration:
slope=g at t=0 t

37. Bouncing ball with energy loss
Let upward vector quantities
be positive.
Falling: with uniform
acceleration a = -g.

38. v-t graph of a bouncing ball
Uniform acceleration: slope = -g v t
falling

39. Bouncing ball with energy loss
Let upward vector quantities
be positive.
Rebound: with large
acceleration a.

40. v-t graph of a bouncing ball
Large acceleration on rebound v
rebound t
falling

41. Bouncing ball with energy loss
Let upward vector quantities
be positive.
Rising: with uniform
acceleration a = -g.

42. v-t graph of a bouncing ball
Uniform acceleration: slope = -g v
rebound
rising t
falling

43. v-t graph of a bouncing ball
The speed is less after rebound
falling and rising have the same acceleration: slope = -g v
rebound
rising t
falling

44. Linear Motion: Motion along a straight line
Uniformly accelerated motion: a = constant
velocity v u
time t

45. Uniformly accelerated motion
u = initial velocity (velocity at time = 0).
v = final velocity (velocity at time = t).
a = acceleration
v = u + at

46. Uniformly accelerated motion
= average velocity
velocity v u
time t

47. Uniformly accelerated motion
s = displacement =
velocity v u
time t
s = area below the graph

48. Equations of uniformly accelerated motion

49. Uniformly accelerated motion
Example 17

50. Free falling: uniformly accelerated motion
Let downward vector quantities be negative
a = -g

51. Free falling: uniformly accelerated motion
a = -g

52. Free falling: uniformly accelerated motion
Example 18

53. Parabolic Motion Two dimensional motion under constant acceleration.
There is acceleration perpendicular to the initial velocity
Examples:
Projectile motion under gravity.
Electron moves into a uniform electric field.

54. Monkey and Hunter Experiment
electromagnet
gun
aluminium
foil
bullet
iron ball

55. Monkey and Hunter Experiment
electromagnet
gun
aluminium
foil
bullet
iron ball
The bullet breaks the aluminium foil.

56. Monkey and Hunter Experiment
electromagnet
gun
bullet
iron ball
Bullet moves under gravity.
Iron ball begins to drop.

57. Monkey and Hunter Experiment
electromagnet
gun
bullet
Bullet is moving under gravity.
Iron ball is dropping under gravity.

58. Monkey and Hunter Experiment
electromagnet
gun

59. Monkey and Hunter Experiment
electromagnet
gun
The bullet hits the ball!

60. Monkey and Hunter Experiment
The vertical motions of both the bullet and the iron are the same.
The vertical motion of the bullet is independent of its horizontal motion.

61. Projectile trajectoryx

62. Projectile trajectoryx

63. Projectile trajectoryu  x
u = initial velocity
 = initial angle of inclination

64. Projectile trajectoryv 
Horizontal line u  x
v = velocity at time t
 = angle of velocity to the horizontal at time t

65. Projectile trajectoryu  x
= x-component of u
= y-component of u

66. Projectile trajectoryu  x

67. Projectile trajectory: accelerationsu  x

68. Projectile trajectoryv 
Horizontal line u
vertical line  x
= x-component of v
= y-component of v

69. Projectile trajectory: velocity in horizontal direction
Horizontal line u  x 

70. Projectile trajectory: velocity in vertical direction
Horizontal line u
vertical line  x

71. Projectile trajectory: displacement
s = displacement y s x
x = x-component of s
y = y-component of s

72. Projectile trajectory: horizontal displacement
s = displacement y s x

73. Projectile trajectory: vertical displacement
s = displacement y s x

74. Equation of trajectory: a parabolic path
s = displacement y s x

75. Projectile trajectory: direction of motionv 
Horizontal line u
vertical line 
Projectile trajectory x
Angle  represents the direction
of motion at time t.

76. Projectile trajectory: direction of motionv 
Horizontal line u
vertical line 
Projectile trajectory x

77. Projectile trajectory
Example 19

78. Projectile trajectory: maximum height H x 
At H, = 0

79. Projectile trajectory: range Ru  R x 
At R, y = 0

80. Projectile trajectory: maximum range Rmax
Rmax x
is maximum when

81. Projectile trajectory: maximum range Rmax
Rmax x
R is maximum when

82. Projectile trajectory: maximum range Rmax
Rmax x

83. Projectile trajectory: time of flight tou to  R x
At time= to , y = 0 

84. Projectile trajectory: two angles for one rangeu u 2 1 R x
1= 2