Chapter 8 Vectors

Physics 504

Scalars and Vectors A scalar quantity has a size and unit.

E.g. 16 N (Newtons) A vector quantity has a size, unit and direction.

E.g. 5 km/h [N] (North)

Distance and Displacement

Distance travelled depends on position.

Distance is a scalar quantity.

It is always positive. E.g. d = 5 km

Distance and Displacement

Displacement depends on the new position compared to the old position.

Displacement is a vector quantity.

E.g. Δd or đ = 5 km North

Exam QuestionThe following graph represents the trail followed by a hiker going from A to F (A –> B –> C –> D –> E –> F). One centimetre represents 100 metres.

A

B C

DE

F

What is the displacement of the hiker?

A) 1 700 m

B)

700 m

C)

500 m

D)

200 m

The Cardinal Points

Cardinal Points II Never Eat Slimey Worms ½ way between North [N] andWest [W] is NorthWest [NW]

½ way between NW and N is NNW

Trigonometric Direction [East] = 0° [North] = 90° [West] = 180° [South] = 270°

Cardinal and Degrees [N 45 ° E] means you start at North and turn 45 ° East.

It is also known as NE. Or as 45 °

Vector Addition We can show vectors as arrows in diagrams.

We add vectors tip to tail. Vector Ả +Vector B = Vector B + Vector Ả The result of adding two or more vectors is

the RESULTANT VECTOR. Vectors are written with little arrows on

top.

Vector Diagrams

Vector Subtraction To subtract a vector from another, you add the opposite.

Vector A – Vector B = Vector A + (-Vector B)

Activity Page 189, Q 1 – 6 Page 192, Q 1 – 3 Page 195, Q 1 – 4 Page 197, Q. 1 - 2

Multiplying Vectors Multiplying vectors only changes magnitude not direction (if positive).

ā = (1,2); 3 ā = (3,6) đ = 5 km 45°; 2đ = 10 km 45°

Vector Division It is just like vector multiplication, but with a fraction.

N.B. multiplying by a negative ř = (3,2); - ř = (-3,-2) Ŝ = 2 m [N]; -ŝ = 2m [S]

x-Component of a Vector ā-hyp opp Θ y-part

adj x – parts Cos θ = adj/hyp = x/ā Thus, x = ā cos θ

y-Component of a Vector ā-hyp opp Θ y-part

adj x – parts sin θ = opp/hyp = x/ā Thus, y = ā sin θ

Addition of Vectors: Component Method

Add the x-components of the vectors together.

Add the y-components of the vectors together.

Add the total x vector to the total y vector tip to tail.

Tools for Solving You can use diagrams; Pythagoras c2 = a2 + b2;

Sine Law Cosine Law SOHCAHTOA

Summary Some motions can be seen easily; other motions must be observed using other senses or devices.

The trajectory is the path of a moving object.

Summary Vector quantities have magnitude and direction.

Scalar quantities only have magnitude.

Displacement, or change in position, is a vector quantity.

Summary Distance, the path length, is a scalar quantity.

Add vectors tip to tail. Page 199, Q 1 - 5

Activity Design an Amazing Race