1. Kinematics and Dynamics
KD1 Vectors

2. Scalar vs. Vector Scalar-Quantity having magnitude only (no direction)
Ex: Temp., mass, time, speed
Vector-Quantity having magnitude AND direction
Ex: Force, displacement, velocity, acceleration

3. Examples: Scalar or Vector?
1) 15 m/s up
2) 21 degrees F
3) 100 watts
4) 50 km N of W
5) 75 mi/hr
Vector
Scalar

4. 3 Ways to Represent Vectors
1. Symbols:
2. Words: 250 m/s East
3. Arrows drawn to scale
Need: a) direction indicator
b) scale: 1 cm=50 m/s
c) directional arrow drawn proper length

5. Example: Represent 250 m/s E : a) direction indicator
b) scale: 1 cm= 50 m/s
c) directional arrow drawn proper length
5 (50 m/s)=250 m/s E
5 cm

6. Vectors
Length of arrow=magnitude
Head of arrow=direction

7. Vectors Components-Vectors whose sum is the resultant
can be simplified into horizontal (X) and vertical (Y) vectors
Resultant-The vector sum of 2 or more components

8. 2 Ways of Finding the Resultant Vector
1. Graphical Method-uses a scale vector drawing
Always add vectors “tail” to “head”
Resultant is drawn from “tail” of 1st to “head” of last vector
EXAMPLES! R

9. Graphical Method
When subtracting vectors, change subtraction to addition
A – B = A + (-B)
The negative (-B) changes the direction of the vector
Negative vectors:
ADD the OPPOSITE direction of the original vector

10. 2 Ways of Finding the Resultant Vector
2. Component Method-Uses calculations to find resultant

11. Trig. Review (Right angles)
Sin=
Cos=
Tan=
Pythagorean Theorem
Coordinate System
Opp / Hyp
Adj / Hyp
Opp / Adj
a2 + b2 = c2

12. Trig.
All vectors can be broken down into horizontal (x) and vertical (y) components
Example:
F=58 N Fy 30 Fx

13. Checks Which color of the Triangle represents the hypotenuse? Blue
Which color of the Triangle represents the opposite side?
Which color of the Triangle represents the adjacent side?
Which color represents the X coordinate?
Which color represents the Y coordinate?
Blue
Green
Red

14. Distance vs. Displacement
How far something move without regards to the direction
(example - 3 miles east and 4 miles north is a total distance of 7 miles)
The change in position of something WITH respects to the direction
(example - 3 miles east and 4 miles north is a total displacement of 5 miles North East
Distance-
Displacement-

15. Steps to Add Vectors by Component Method
1) Break down each vector into x and y components
2) Add similar components
Add all “x” components
Add all “y” components
3) Use Pythagorean theorem to find magnitude of resultant
4) Use tangent function to find angle and direction of resultant

16. EXAMPLES! =
– =

17. Examples
Given the scale and the RED arrow, describe the vector in words (use both magnitude and direction)
1 cm = 5 m/s
Presume the red arrow is 7 cm
Answer = 35 33˚ S of W
OR 35 57˚ W of S

18. Examples Calculate the horizontal (X) and vertical (Y) components.
The vector is representing 35 33˚ S of W
Sin θ = opp / hyp
Sin 33 = opp / 35
.545 = opp / 35
Opp (Y) = 19 m/s
Cos θ = adj / hyp
Cos 33 = adj / 35
.839 = adj / 35
Adj (X) = 29 m/s