Section 4: Mechanics
-Scalars and Vectors
• Scalars are quantity that has no direction – it’s just an amount of something – therefore it only
had magnitude
• Vectors have both size and direction
Scalars Vectors
Length/ distance, speed, mass, temperature, time, Displacement, velocity, force (including weight),
energy acceleration, momentum
Adding vectors together
Adding two or more vectors is called finding their resultant. There are
two ways to find the resultant of vectors.
Using scale diagrams:
The resultant vector can be found by drawing a scale drawing of the
vector, tip-tail, then measuring the length and the angle of the
resultant vector.
Using trigonometry:
If two vectors are perpendicular to one another, you can find the size and angle of the resultant vector
using trigonometry.
Using either – a2 + b2 = c2 or SOHCAHTOA
Resolving vectors into components
Resolving vectors is the opposite of finding the resultant – you start from the resultant vector and then
break it down into two components at right angles from each other.
The components of a vector are perpendicular to each other; hence they form a right-angled triangle.
Trigonometry is needed to find the components of the vector in each direction.
• Horizontal component
Cosθ = A/H
Cosθ = VH (Horizontal Vector) / VA (Resultant Vector)
VH (Horizontal vector) = VA (Vector A) x Cos θ
-Scalars and Vectors
• Scalars are quantity that has no direction – it’s just an amount of something – therefore it only
had magnitude
• Vectors have both size and direction
Scalars Vectors
Length/ distance, speed, mass, temperature, time, Displacement, velocity, force (including weight),
energy acceleration, momentum
Adding vectors together
Adding two or more vectors is called finding their resultant. There are
two ways to find the resultant of vectors.
Using scale diagrams:
The resultant vector can be found by drawing a scale drawing of the
vector, tip-tail, then measuring the length and the angle of the
resultant vector.
Using trigonometry:
If two vectors are perpendicular to one another, you can find the size and angle of the resultant vector
using trigonometry.
Using either – a2 + b2 = c2 or SOHCAHTOA
Resolving vectors into components
Resolving vectors is the opposite of finding the resultant – you start from the resultant vector and then
break it down into two components at right angles from each other.
The components of a vector are perpendicular to each other; hence they form a right-angled triangle.
Trigonometry is needed to find the components of the vector in each direction.
• Horizontal component
Cosθ = A/H
Cosθ = VH (Horizontal Vector) / VA (Resultant Vector)
VH (Horizontal vector) = VA (Vector A) x Cos θ
