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

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 . . .

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?

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

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

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

Vector Subtraction Example: Ex: Vector Sub Vector Subtraction Example:

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

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

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

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

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

Answer 6a y origin x

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

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

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