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Chapter 8: Vectors and Scalars
Please remember to photocopy 4 pages onto one sheet by going A3→A4 and using back to back on the photocopier
A Scalar Quantity is one which has magnitude only. Examples: length, area, energy, time.
A Vector Quantity is one which has both magnitude and direction. Examples: displacement, acceleration, force.
Vectors can be represented on a diagram by an arrow, where the vector is in the same direction as the quantity it is
representing. Composition (addition) of two perpendicular vectors
• When adding two vectors, they should be arranged tail-to-tail (the arrow represents the head) and the rectangle
should then be completed.
• The resultant is the line joining the two tails to the opposite corner.
• The direction is from the tails to the opposite corner.
• Mathematically, the length of the vector can be found by using Pythagoras’ Theorem.
• Mathematically, the angle can be found by using Tan θ = Opp/Adj.
Experiment: To find the Resultant of Two Forces
Attach three Newton Balances to a knot in a piece of thread.
1. Adjust the size and direction of the three forces until the
knot in the thread remains at rest.
2. Read the forces and note the angles.
3. The resultant of any two of the forces can now be shown to be
equal to the magnitude and direction of the third force.
Resolving a vector into two perpendicular Components
You have just seen that two perpendicular vectors can be added together to form a resultant.
Well let’s say we started off with the resultant. Would we be able to get back the two original vectors?
First we need to remember that for a right-angled triangle:
Sin θ = Opposite/Hypothenuse, therefore Opposite = Hypothenuse x Cos θ {Opp = H Sin θ}
Cos θ = Adjacent/Hypothenuse, therefore Adjacent = Hypothenuse x Cos θ {Adj = H Cos θ}
Example
Consider a velocity vector representing a velocity of 50 ms-1, travelling at an angle of 600 to the
horizontal:
The Opposite is equal to H Sin θ, which in this case = 50 Cos 600 = 43 ms-1.
The Adjacent is equal to H Cos θ, which in this case = 50 Sin 600 = 25 ms-1.
Leaving Cert Physics Syllabus: Vectors and Scalars
Content
Depth of Treatment
Activities
STS
Vectors and Scalars
Distinction between
vector and scalar
quantities.
Vector nature of physical
quantities: everyday
examples.
Composition of
perpendicular vectors.
Find resultant using
newton balances or
pulleys.
Resolution of co-planar
vectors.
Appropriate
calculations.
