Starter Physics - Basic Maths

Basic Maths

How we use maths in physics.

From an early age we are taught to use maths operators: add (+), subtract (-), multiply (x), and divide (÷).
In physics (or other sciences) we don't normally use the multiply (x) or divide (÷) symbols in equations.
When we want to multiply, as in A = B x C, we usually write A = BC.
Sometimes we put a dot between: A = B.C to make it obvious we want to multiply.
Writing a series of letters next to each other means we multiply them together.
When we want to divide we write the numbers as a fraction, so E = F ÷ G becomes E = F/G.
Putting these ideas together: H = (I x J) ÷ (K x L) is written as H = IJ/(KL).
If needed, brackets can be used to show the order of calculation: M = (1 + N)P/(QR), where the things in brackets are calculated first.

In physics (or other sciences) we sometimes use negative numbers.
Negative numbers are numbers below zero.
An object moving in a positive direction might be going to the right, but if it is going to the left then we can say it is moving in a negative direction.
If an object moved from zero, two units to the right, it would be at position +2
If we then move that object 5 units to the left, it would be at position -3

When a number is multiplied by itself, we show this with a number which shows the number of times it is multiplied: A x A = A² or A x A x A = A³etc.
If we have a fraction or division of two powers we can write them more simply as follows:

(A x A)/(B x B x B) = A² / B³= A².B^-3

A negative power means that it belongs at the bottom of the fraction (the denominator).

When a force acts in a particular direction we can say that it only affects movement in that direction.
If a force is only acting up-or-down then we can say it does not affect the movement left-or right.
This helps us to simplify physics problems, like the movement of objects in gravity, because the force of gravity is only 'downwards'.
The movement left-or-right is not affected by the force of gravity.
So the equations for the vertical axis (up-or-down) will be different from those for the horizontal axis (left-or-right) and can be calculated separately.
They can then be combined later to find the overall speed and direction of the object.

When a number is very large or very small we might want to simplify how we write it.
For example, when we talk about 200,000,000 Joules we can simplify it to 200MegaJoules.
In this case, Mega means million (or 1,000,000).
Some more examples are:

1,000,000,000 = Giga (or 1x10⁹)

1,000,000 = Mega (or 1x10⁶)

1,000 = kilo (or 1x10³)

0.001 = milli (or 1x10^-³)

0.000001 = micro (or 1x10^-6)

0.000000001 = nano (or 1x10^-⁹)

Scientists uses this as a kind of shorthand, to avoid writing out lots of zeros.
We can also use scientific notation, i.e. 6,000,000 = 6x10⁶ which means 6 followed by 6 zeros.
If it is 6x10^-6 then we move the decimal point 6 places to the left = 0.000006.