Homogeneity of Physical Equations & Powers of Ten (OCR A Level Physics)
Revision Note
Units
In Physics, every quantity has an appropriate unit
It is important that the correct unit is applied to that quantity
Table of Units
A unit to the power of –1 (–1) means ‘per’ eg. per metre = m–1
If this is to the power of –2 or above, this means 'per' quantity squared eg. per unit area = m–2
Units of constants will be given on the data sheet
There are a few cases when values have no units, these are:
When the value is calculated from a trigonometric function eg. cos(ωt)
Ratios, where both quantities have the same units eg. v / c
A number of something eg. number of molecules
Examiner Tips and Tricks
Not all exam questions will provide the unit, and a mark is often allocated for this in a calculation. Always write your answer in SI units, unless stated otherwiseNot checking units carefully when calculating values from a graph or table is very common mistake. Make sure to check the units on the axes and if they match the equation you are using.
Homogeneity of Physical Equations
An important skill is to be able to check the homogeneity of physical equations using the SI base units
The units on either side of the equation should be the same
To check the homogeneity of physical equations:
Check the units on both sides of an equation
Determine if they are equal
If they do not match, the equation will need to be adjusted
How to check the homogeneity of physical equations
Powers of Ten
Physical quantities can span a huge range of values
For example, the diameter of an atom is about 10–10 m (0.0000000001 m), whereas the width of a galaxy may be about 1021 m (1 000 000 000 000 000 000 000 m)
This is a difference of 31 powers of ten
Powers of ten are numbers that can be achieved by multiplying 10 times itself
It is useful to know the prefixes for certain powers of ten
Powers of Ten Table
Examiner Tips and Tricks
You will often see very large or very small numbers categorised by powers of ten, so it is very important you become familiar with these as getting these prefixes wrong is a very common exam mistake!
There is also a power of ten known as a Femto− (f) which is equal to 10−15, knowledge of this is not required according to the OCR specification, however, it has been known to crop up occasionally so make sure you are aware of the Femto (f) too!
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