1. Displacement and Velocity
Vectors in Math Land
Vectors in Physics Land
Outline

2. Scalars vs. vectors Scalar : a real number, no “direction”
Scalar vs. Vector
Scalars vs. vectors
Scalar : a real number, no “direction”
Examples : mass, charge, energy,
temperature, time . . .
Vector : a scalar (its magnitude) and a direction in space
Examples : position displacement, velocity,
force, torque, momentum . . .

3. Vectors have different rules of arithmetic
If you add 2 students to a group of 3 students, how many
students do you have?
If you walk North 3 km and then walk West 4 km, what is your displacement from where you started?

4. We will use the Triangle Method
Vector Addition:
Vector + Vector = Vector
We will use the Triangle Method

5. Vector Multiplication:
i) scalar  vector = vector
Not in this course…
ii) vector  vector = scalar (dot product)
iii) vector  vector = vector (cross product)

6. 3 – 2 = 3 + (-2) Just like: Vector Subtraction:
Vector - Vector = Vector
Just like:
3 – 2 = 3 + (-2)

7. Vector Subtraction Example:
Ex: Vector Sub
Vector Subtraction Example:

8. Position Vectors
Tells where something is relative to the origin of position graph (usually 2-D or 3-D)
The origin is just a convenient choice of place to measure from
The origin could be anywhere, but if you choose it carefully, you will likely end up doing less work
A position vector is ALWAYS measured from the ORIGIN

9. What do you need to define a position?
Position Vectors Ex
Demo: use tape measures to lay out the x and y axis on the floor x y
What do you need to define a position?
origin

10. Displacement
The point of making position vectors is to make it easier to discuss how things CHANGE their positions
A change in position is called a displacement
The displacement vector is typically written as
Displacement is not always measured from the origin!
A displacement vector is ALWAYS measured from the tip of the initial position vector to the tip of the final position vector

11. Delta   Greek letter for capital D
Physicists use it to represent “change” in a quantity
Note that:
Where there is a , subtraction is always involved

12. QQ6a r
A person starts at position 1 and ends at position 2, what is their displacement? x y

13. Answer 6a y
origin x

14. QQ6c r
A person starts at the origin and walks to position (10, 10), stops and then walks to position (30,10). What is their displacement from the origin? y
(10,10)
(30,10)
origin x

15. y If , what was ? (10,10) (30,10) origin x r1 is a zero length vector.
Answer 6c
QQ6c r y If
, what was ?
(10,10)
(30,10)
r1 is a zero length vector.
origin x

16. Do for next class: Read: sections 1.4, 1.5, 1.6
Suggested problems: 1.10, 1.16