Scalars and Vectors - Concept, Applications, & Examples (IGCSE exam 2023)
Channel: Physics Partner
Date: 06/08/2022

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The IGCSE Physics syllabus has been reviewed and revised for first examination in 2023. All quantities in Physics can be divided into scalars and vectors and you need to recognize if a quantity is one or the other for your IGCSEs (Vector addition is the new topic in this curriculum) and vectors become particularly important for anyone considering taking Physics to A-level and beyond. 
What are scalars and vectors?
Physics is a mathematical science. The underlying concepts and principles have a mathematical basis. Throughout the course of our study of physics, we will encounter a variety of concepts that have a mathematical basis associated with them. While our emphasis will often be upon the conceptual nature of physics, we will give considerable and persistent attention to its mathematical aspect.
The motion of objects can be described by words. Even a person without a background in physics has a collection of words that can be used to describe moving objects. Words and phrases such as going fast, stopped, slowing down, speeding up, and turning provide a enough vocabulary for describing the motion of objects. In physics, we use these words and many more. We will be expanding upon this vocabulary list with words such as distance, displacement, speed, velocity, and acceleration. As we will soon see, these words are associated with mathematical quantities that have strict definitions. The mathematical quantities that are used to describe the motion of objects can be divided into two categories. The quantity is either a vector or a scalar. These two categories can be distinguished from one another by their distinct definitions:

Money for example will have a quantity eg €4.56 but not a direction. You can´t say €4.56 in the direction 40º North of East !! Mass also has no direction as it is simply a quantity of material, the combined number of particles an object is made up of. We call those quantities which have a magnitude but no direction scalar quantities.

There are many scalar quantities, for example:

Distance, speed, time, power, energy
Scalar quantities change when their magnitude changes.
Weight on the other hand does have a direction. Weight is the combined effect of a mass finding itself in a gravitational field.  When a mass finds itself in a gravitational field the resulting quantity is known as weight which now has a direction as well as a magnitude (size). So a quantity which is a product of a scalar and a vector has also got to be a vector since one component of it has a direction the resulting product too will have a direction.
These are six vector quantities:
Displacement,velocity,acceleration,force,weight,momentum
Vector quantities change when:
their magnitude changes,their direction changes, their magnitude and direction both change
Your weight W/mg (either version is correct) always acts towards the center of the Earth. Don´t forget from our last post that the unit for weight the Newton N can also be written as Kgms^2.  The gravitational field strength g has units of either Nkg^-1 or ms^-2 (which are the same as those for acceleration).  The gravitational field acts as a constant downward force on us which is sometimes easy to forget, until you have to climb to the top of 3 flights of stairs again.
The Earth´s gravitational field strength acts downwards with a magnitude of 9.81 Newtons for every kilogram of mass present ie NKg^-1.  If your bag is made up of 10kg of bag particles and you leave it in a place where there is a gravitational field (Nkg^-1 or ms^-2) ie anywhere on Earth, the effect of the gravitational field on the bag will be 9.81Nkg^-1 x 10kg.  When doing a multiplication both number and unit get multiplied so we have 9.81 x 10 = 98.1 and the unit Nkg^-1 x kg and we can see that the kg cancel out leaving us with N and so the answer is 98.1N.
Acceleration at a constant speed is often cited as an example of a vector quantity changing.  Well, we know that acceleration means change and we know that the speed is constant so that means that it must be the direction that is changing. The vector version of speed is velocity. The example often given is of a cyclist going around a circular track at a steady speed but always changing direction.
A geostationary satellite is in orbit above the Earth. It moves at constant speed but its velocity is constantly changing (since its direction is always changing). If its velocity is changing we say that it is accelerating. Remember, acceleration always means that some change is taking place!
The difference in two vectors quantities = final vector – initial vector
The difference in two scalar quantities = large value – small value