1. Motion
Kinematics

2. Physics
Physics – a study of matter and energy with an emphasis on energy
Mechanics – a branch of physics that deals with a study of motion, there are 2 types

3. Motion

4. Types of Motion Kinematics – a study of how objects move
Types of motion are:
Uniform
Accelerated
Free-fall
Projectile
Circular
Harmonic
Dynamics – a study of why objects move
Quantitative studies of why objects move began with Newton
Motion is broken up into 2 different types
Uniform Motion – movement at a constant speed in a straight line
Nonuniform Motion – movement that involves a change in speed, direction, or both

5. Significant Digits
When we do calculations, we must look at the accuracy and precision of the results.
To do this, we have some simple rules to follow that are called Significant Digits or Significant figures
These are very important and if done incorrectly will cost you marks on assignments, quizzes, and tests

6. Sig Digs, Sig Figs…etc.
Sig Figs tell us how many digits we can have in our answers.
The numbers 1 through 9 are significant all the time, but 0 is a special case.
has 4 sig figs
1.92 – has 3 sig figs
1.201 x 104 has 4 sig figs
has 3 sig figs
If a 0 comes before a decimal or directly after, it is not significant

7. Sig Figs – Addition/Subtraction
What about calculations then??
Addition/subtraction
Take the number with the least number of decimal places to make the final answer
= Sig figs – 32.4

8. Sig Figs – Multiplication/Division
In multiplication and division, you take the smallest number of significant digits
3.14 * 2.2
= 6.908
Sig figs = 6.9

9. Base Units for this course
Time – the base units are seconds (s)
Length – the base units are metres (m)
Mass – the base units are kilograms (kg)
All other measurements are typically taken in these units or some variation of them and are called Derived Units

10. Scientific Notation
When your values get too large, which will happen a lot, you need to be able to display them in a compact form, Scientific Notation
– 1.23x108
– 4.79x10-3
When you have large or very small numbers, it is expected you use Scientific Notation

11. Quantities
There are 2 types of quantities that you are going to look at for the rest of your physics career.
Scalars
Vectors

12. Scalar Quantities
Scalar quantities are things like speedometer, speed limits, a measurement on a ruler, etc.
Each of these is a measurement, but they are only have units and do not give you a direction
Any number that is not given a direction but has units is a Scalar Quantity

13. Vector Quantities
If a measurement is given a direction, then it is a vector quantity.
Does the direction really matter?
Yes, it allows you to determine if something is positive or negative

14. Vectors
Vector Quantity – tells you “how much” (magnitude) and direction
Must be denoted with a vector arrow
Must also be given a sign, either positive or negative according to the following grid

15. How to give direction X-axis Method
This is measured from the positive x axis counter-clockwise
Navigator Method
This is measured from the North, clockwise

16. Examples X-axis Method 34.2 m/s [34° above the horizontal]
1.24x103 N [283°]
Navigator Method
34.2 m/s [34° N of E]
34.2 m/s [56° E of N]
1.24x103 N [13° N of W]
1.24x103 N [77° W of N]

17. Distance and Displacement
Distance “d”
Indicates how far something is from a starting point or a reference point
Distance travelled “Δd”
Indicates how far or the total distance an object has travelled from a starting point
Δd = Δd1 + Δd2
Position “d”
Indicates how far something is from a starting point or a reference point and in what direction
Displacement “Δd”
Indicates the change in position or how far an object has travelled from a stating point and in what direction
Δd = Δd1 + Δd2

18. Speed Instantaneous Average
This is the speed calculated at a particular point.
Ex: at some point on a road you car may be travelling 100 km/h
You get these measurements by directly looking at your speedometer
Average
This takes into account the total distance travelled and the total time travelled
Ex: on a road trip, you travel for 2.5 hours and cover a distance of 328 km. You have an average speed of km/h
It is calculated using vav =d/t

19. Which “d” is it? Distance “d” Position ” “ Distance traveled ”Δd”
Indicates how far something is from a starting point or a reference point
Position ” “
Indicates how far something is from a starting point or a reference point and in what direction
Distance traveled ”Δd”
Indicates how far or the total distance an object has traveled from a starting point
Δd = Δd1 + Δd2
Displacement “ “
Indicates the change in position or how far an object has traveled from a starting point and in what direction

20. Time, Velocity, and Speed
Time “Dt”
Indicates the total time elapsed
Average Speed “v”
Indicates the rate or how fast something is traveling
Can be calculated using
Average Velocity “v”
Indicates the rate or how fast something is traveling and the direction

21. 1 Dimensional Uniform Motion – traveling in 1 direction
An object travels 10.0 m in 5.00s. Find the average speed.
An object travels 15.0m [E] in 5.00s. Find the average velocity
A person starts from position A and walks 10.0m [E] to position B in 5.00s. Find Δd,Δd,v,v

22. 1 Dimensional Uniform Motion – traveling in 2 directions
A person starts at A and walks 10.0m [E] in 5.00s then 15.0m [W] in another 8.00s. Find Δd,Δd,v,v.
An object travels at 5.00 m/s [E] for 5.00s, then at 2.00 m/s [E] for 3.00s.
Find Δd,Δd,v,v
Look at doing a lab here with the air track on velocity, and acceleration: see text for labs

23. Multiple Vectors
What happens if you have to add multiple vectors together?
You can draw out each vector, and place them together (as arrows), with the tip of the first touching the tail of the second, and so on.

24. Multiple Vectors Cont’d
Once you have placed all the vectors together, the resultant vector is the displacement of the object.
The resultant is found by placing a line from the starting point to the tip of the last arrow, and then use Trig to help you out.

25. Resultant Displacement
How do you deal with the following?
A person travels 1.7 km [E] then turns and travels 2.1 km [S]. What is the person’s displacement?
First draw a diagram to help
Dd1 =1.7 km [E]
Hw: p.20 #’s 2-5 and p. 24 #’s 1-3
Dd2 =2.1 km [S]
DdR =2.7 km [51° S of E]

26. Graphing
Graphing is one method of representing the motion of an object.
There are 2 different types of graph that we will look at
Position – time
Velocity – time

27. Position – Time Graphs
If a car was traveling East at +10 m/s, the car undergoes constant velocity giving a positive slope to the upper right
If the same car was traveling at a changing velocity to the right, the graph would still be positive

28. Is Slope Important?
You bet it is. The slope of the p-t graph gives important information about the problem.
Constant slope (straight line) – constant velocity
Changing slope (curved line) – acceleration
Steep slope – fast velocity
Shallow slope – slow velocity

29. Curved Slopes A curved line is a sign of accelerated motion
The first image shows an object with a small, negative velocity and finishes with a large negative velocity
The second image shows a large negative slope that changes to a small velocity at the end.
The first diagram shows a small negative slope which changes to a larger velocity is a negative direction. The object is speeding up towards it’s reference point. We call this negative acceleration
The graph on the right shows an object with a high, negative velocity and finishes with a small velocity that is positive. This is because the slope is going from negative to flat which means that it is a positive slope at the bottom

30. Slope Continued What happens if a line is horizontal?
In this case, the object is stationary
In the example below, at the 5 second mark, the object comes to a complete stop for 5 seconds

31. How do you find the slope?
We find the slope of a p-t graph the same way we would find the slope in a mathematical graph

32. Velocity – Time Graphs
If a car was traveling East at +10 m/s, the car undergoes constant velocity, a v-t graph would look like this
If the same car was traveling at a changing velocity to the right, the v-t graph would look like the following

33. Slopes and V-T Graphs
Slopes are very important when looking at V-T graphs
There are 2 types of motion
Constant velocity
Accelerated velocity

34. Slopes Constant Velocity Acceleration
These are always horizontal lines at the velocity
If it is above 0, it is positive, below 0 it is negative
Acceleration
Positive
All accelerations are positive if the line is on the positive side
All accelerations are negative if they are on the negative side

35. Slopes
In an v-t graph, we also need to know if an object is speeding up or slowing down.
How can we determine this?

36. What else can we get from VT?
We can get other information other than acceleration from a v-t graph.
We can also get the displacement of the object
This is done by calculating the area under the curve

37. The Other Method
There will be more times in Physics, where you will not have a graph to help you out.
When this happens, we have some equations to help us out.

38. Kinematic Equations
See p.44 for more information

39. Kinematic Equations
The previous equations were given for scalar calculations
You can have the same equations for vector quantities
These are shown with the variables having a line above each one

40. Projectile Motion

41. What is Projectile Motion?

42. Instructional Objectives:
Students will be able to:
Define Projectile Motion
Distinguish between the different types of projectile motion
Apply the concept to a toy car and measure its velocity

43. What is a projectile?
Projectile -Any object which projected by some means and continues to move due to its own inertia (mass).

44. Projectile Motion Two-dimensional motion of an object Vertical
Horizontal

45. Projectiles move in TWO dimensions
Since a projectile moves in 2-dimensions, it therefore has 2 components just like a resultant vector.
Horizontal and Vertical

46. Types of Projectile Motion
Horizontal
Motion of a ball rolling freely along a level surface
Horizontal velocity is ALWAYS constant
Vertical
Motion of a freely falling object
Force due to gravity
Vertical component of velocity changes with time
Parabolic
Path traced by an object accelerating only in the vertical direction while moving at constant horizontal velocity

47. Horizontal “Velocity” Component
NEVER changes, covers equal displacements in equal time periods. This means the initial horizontal velocity equals the final horizontal velocity
In other words, the horizontal velocity is CONSTANT. BUT WHY?
Gravity DOES NOT work horizontally to increase or decrease the velocity.

48. Vertical “Velocity” Component
Changes (due to gravity), does NOT cover equal displacements in equal time periods.
Both the MAGNITUDE and DIRECTION change. As the projectile moves up the MAGNITUDE DECREASES and its direction is UPWARD. As it moves down the MAGNITUDE INCREASES and the direction is DOWNWARD.

49. Combining the Components
Together, these components produce what is called a trajectory or path. This path is parabolic in nature.
Component
Magnitude
Direction
Horizontal
Constant
Vertical
Changes

50. Examples of Projectile Motion
Launching a Cannon ball

51. Horizontally Launched Projectiles
Projectiles which have NO upward trajectory and NO initial VERTICAL velocity.

52. Horizontally Launched Projectiles
To analyze a projectile in 2 dimensions we need 2 equations. One for the “x” direction and one for the “y” direction. And for this we use kinematic #2.
Remember, the velocity is CONSTANT horizontally, so that means the acceleration is ZERO!
Remember that since the projectile is launched horizontally, the INITIAL VERTICAL VELOCITY is equal to ZERO.

53. Horizontally Launched Projectiles
Example: A plane traveling with a horizontal velocity of 100 m/s is 500 m above the ground. At some point the pilot decides to drop some supplies to designated target below. (a) How long is the drop in the air? (b) How far away from point where it was launched will it land?
What do I know?
What I want to know?
vox=100 m/s
t = ?
y = 500 m
x = ?
voy= 0 m/s
g = -9.8 m/s/s
1010 m
10.1 seconds

55. Vertically Launched Projectiles
NO Vertical Velocity at the top of the trajectory.
Vertical Velocity decreases on the way upward
Vertical Velocity increases on the way down,
Horizontal Velocity is constant
Component
Magnitude
Direction
Horizontal
Constant
Vertical
Decreases up, top, Increases down
Changes

56. Vertically Launched Projectiles
Since the projectile was launched at a angle, the velocity MUST be broken into components!!! vo
voy q
vox

57. Equations
X- Component
Y- Component
Vectors
Note: g= 9.8 m/s^2

58. Vertically Launched Projectiles
There are several things you must consider when doing these types of projectiles besides using components. If it begins and ends at ground level, the “y” displacement is ZERO: y = 0

59. Vertically Launched Projectiles
You will still use kinematic #2, but YOU MUST use COMPONENTS in the equation. vo
voy q
vox

60. Example
A place kicker kicks a football with a velocity of 20.0 m/s and at an angle of 53 degrees.
(a) How long is the ball in the air?
(b) How far away does it land?
(c) How high does it travel?
vo=20.0 m/s
q = 53

61. Example
What I know
What I want to know
vox=12.04 m/s
t = ?
voy=15.97 m/s
x = ?
y = 0
ymax=?
g = m/s/s
A place kicker kicks a football with a velocity of 20.0 m/s and at an angle of 53 degrees.
(a) How long is the ball in the air?
3.26 s

62. Example
A place kicker kicks a football with a velocity of 20.0 m/s and at an angle of 53 degrees.
(b) How far away does it land?
What I know
What I want to know
vox=12.04 m/s
t = 3.26 s
voy=15.97 m/s
x = ?
y = 0
ymax=?
g = m/s/s
39.24 m

63. Example What I know What I want to know t = 3.26 s x = 39.24 m y = 0
vox=12.04 m/s
t = 3.26 s
voy=15.97 m/s
x = m
y = 0
ymax=?
g = m/s/s
A place kicker kicks a football with a velocity of 20.0 m/s and at an angle of 53 degrees.
(c) How high does it travel?
CUT YOUR TIME IN HALF!
13.01 m

64. Factors Affecting Projectile Motion
What two factors would affect projectile motion?
Angle
Initial velocity
Visual
Initial Velocity
Angle

65. Example
An object is fired from the ground at 100 meters per second at an angle of 30 degrees with the horizontal
Calculate the horizontal and vertical components of the initial velocity
After 2.0 seconds, how far has the object traveled in the horizontal direction?
How high is the object at this point?

66. Solution
Part a
Part b
Part c

67. Applications
Any Ideas?