SCALAR AN VECTOR QUANTITIES Lesson Note

LEARNING OBJECTIVES: By the end of the class, students should be able to :

DEFINITION:

SCALAR QUANTITIES: A scalar quantity is one which has only magnitude. Examples are distance, speed, Temperature, Volume, Mass etc.

VECTOR QUANTITIES: A vector quantity is one which has both magnitude and direction. Example include: displacement, velocity, weight, force, acceleration etc.

Scalar can be added and subtracted easily by using ordinary algebra. While vector involve mathematical calculation using vector diagram.

REPRESENTATION OF A VECTOR

Vector representative may be referred to as a way of representing vector either graphically or analytically

PARALLELOGRAM LAW OF VECTOR

The states that if two vectors acting at a point are represented in magnitude and direction by two adjacent sides of a parallelogram starting from the same point, their resultant vector is represented by the diagonal passing through that same point

Parallelogram law of vector

In ACD

AC² = OB² + OA² + 2(OB)(OA) cos(180-)

N:B = cos(180-) = -cos

Where 0<<90

Worked Example: Find by the means of vector diagram he resultant of two force of 7N and 3N acting perpendicular

B

7N

A 3N O

|OB|² = |AB|² + |OA|²

|OB|² = |7|² + |3|²

|OB|² = 49 + 9 = 58

tanθ = 7/3.

= 7/3 66.8

+ + 90 = 180

66.8 + + 90 = 180

∝= 180-156.8

= 23.19

Example: Solve this using resolution into component forces. To find the resultant of more than two vector, we resolve each vector of more perpendicular direction. Add all the horizontal component X, an all the vertical component Y. For example

F₂ F₁

2

3 4

F₄ F₃

X = F₁cos ₁ +(-F₂cos ₂) + (-F₃cos ₃) + F₄cos ₄

Y = F₁sin₁ + F₂sin ₂ + F₃cos ₃ + F₄cos ₄

R² = X² + Y²