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 and vectors become particularly important for anyone considering taking Physics to A-level and beyond.

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.

There are only 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

This video best matches the IGCSE and A-level content required by your Physics course. It is just over 10 minutes long and should give you a better understanding of Scalars and Vectors.

See you next week !!

Alex Mitchell


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