Scalars and Vectors

Scalar

• A SCALAR is ANY quantity in physics that has MAGNITUDE, but NOT a direction associated with it.• Magnitude – A numerical

value with units.

ScalarExample

Magnitude

Speed 20 m/sDistance 10 mAge 15 yearsHeat 1000

calories

Vector• A VECTOR is ANY quantity in

physics that has BOTH MAGNITUDE and DIRECTION.

v, x, a, F

Vectors are typically illustrated by drawing an ARROW above the symbol. The arrow is used to convey direction and magnitude.

Vector Magnitude and Direction

Velocity 20 m/s, N

Acceleration 10 m/s2, E

Force 5 N, W

Q: How would you describe the birds movement?

1 meter

45◦

A• The arrow is the

representation of the displacement of bird

• It is a vector, denoted by the arrow over the symbol

• The symbols |A| and A represent the magnitude of the vector A

A: It went 1 meter in a straight path at an angle of 45°

Vector Notation

• An effective and popular system used in physics is called unit vector notation. It is used to denote vectors with an x-y Cartesian coordinate system.

Vector Addition (Collinear)

Vector Subtraction

Non-Collinear Vectors

Determining θ

Determining a missing component