SI units (2.1.2)
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The International System of Units (SI) is the standard set of units used by physicists and other scientists for measurements.
SI consists of seven quantities and their corresponding units, known as the SI base units, which are shown in the table below.
The SI base unit symbols are written in lowercase letters, except the symbols named after a person: kelvin has the symbol and the ampere has the symbol
There are many other physical quantities that can be measured, other than those corresponding to the SI base units.
Speed, acceleration, and force are examples of derived units. These quantities are known as derived quantities and are measured in derived units, which can be determined by substituting the base units into the equation that relates the derived quantity to the base quantities.
An example of this can be seen from the speed equation:
Where:
- is speed,
- is the distance travelled in a straight line, and
- is the time taken.
Substituting the base units for length and time leads to:
Question walkthrough
Deriving the Base Units of Density
Derives the SI base units of density by substituting the base units of mass and volume into the equation ρ = M/V.
Many derived units are used so frequently in measurements that they have been given specific names. A few of the most useful derived units are shown in the table below.
It is useful to note that it is much more convenient to use these abbreviated units rather than write out the full SI units during calculations. All of the above units are capitalised since they are named after people.
Physical equations must have the same units on either side: in other words, they must be homogeneous. The homogeneity of a physical equation can be checked by substituting SI base units into either side of the equation to ensure that both sides result in the same combination of SI units.
An example of this can be demonstrated with an equation of motion for uniform acceleration:
Velocity on the LHS of the equation has SI base units of For on the RHS, SI base units must be substituted for initial velocity , acceleration and time
It is important to note that the numerical coefficient of 2 is dropped, as pure numbers are dimensionless. The equation is homogeneous:
Prefixes are used to represent decimal submultiples or multiples of SI units in compact form.
For example:,
- can instead be written as and
- is equal to
A list of the most useful prefixes required for your exams is shown in the table below.
All the prefixes with a multiplication factor greater than one are in uppercase, with the exception of kilo, whereas all the prefixes with a multiplication factor less than one are in lowercase.
When recording data in a table, the independent variable data points are listed in the first column, and the dependent variable data points are listed in the second column (for quantitative measurements).
Both column headings should include the SI units for the variable in brackets.
The table above shows the measurements of an object’s speed in a straight line against time.
Note that milliseconds are used for time so that the standard form is not required in the table.
The number of significant figures used for each variable depends on the precision of the measuring equipment.
When data from tables is plotted as a graph, the independent variable is plotted on the Y axis and the dependent variable on the X axis.
The graph on the left is less useful since the data points would ideally fill more than half the graph in both the X and Y directions.
In the graph on the right, the scale of the Y axis has been adjusted using a false origin (an origin that is not zero) to better highlight the relevant data points and the line of best fit.