O Level Physics Notes: Scalars and Vectors
Scalar quantities are quantities that need only a number to describe them fully.
Examples include:
mass, speed, distance, power, energy.
Vector quantities are quantities that have both number and direction. Examples
include: velocity, displacement, force, acceleration.
Some scalar quantities have commonly used vector versions. For example, we may
use either speed or velocity in conversation, and when we speak of distance, which is
a scalar, we usually mean the distance from somewhere to somewhere else, which
makes it a vector.
The distance from London to Birmingham is 101 miles, and 101 miles is a scalar, but
to travel from London to Birmingham we can't start from London and go in any
direction – we have to travel north west, and this pairing of distance with direction
defines a vector.
If we take 2 hours to travel from London to Birmingham, the speed is
and this is a scalar, but we must travel in the direction
north west, and this pairing of speed with direction defines a vector.
|Scalars can be added or subtracted with no complications. Masses of 3Kg and 5Kg
together make a mass of 8Kg, but we have to be careful about adding vectors. Adding
a force of 3N directed North to a force of 5N directed north east is best illustrated by
drawing a triangle.
We construct a parallelogram as shown.
Now draw in the diagonal so that it represents the sum of the two vectors.
We can use the triangle ABC to find the resultant R using the cosine rule.
We can also find the bearing, given by the angle
using the sine rule:
O Level Physics Notes: Moments – The Lever Principle
The principle of moments can be used to move large objects with manageable forces.
The Law behind 'The Lever Principle', famously summarised by Archimedes of
Syracuse in the phrase, 'Give me a place to stand and I will move the Earth'. To apply
the principle of moments, we choose a point to take moments about. A natural point to
take moments about is a point about which turning might take place. In the diagram
below this is the point O.
Taking moments about a point means working out the product of force and
perpendicular distance for the anticlockwise forces:
And putting them equal to the product of force and perpendicular distance for the
clockwise forces:
obating the equation
Knowledge of any three of
will mean we can work out the other one.
The Lever Principle is illustrated below. Taking moments about the balance point,
This means we can use a force of 653N to lift a weight of 1000*9.8=9800N.