Measurement, units and uncertaintyIB MYP Physics: Revision notes

Scientists around the world use the SI system so that measurements mean the same everywhere. The base units you need are the metre (m) for length, kilogram (kg) for mass, second (s) for time, ampere (A) for current and kelvin (K) for temperature.

Derived units are made by combining base units:

• newton (N), the unit of force (1 N = 1 kg m/s²)
• joule (J), the unit of energy
• watt (W), the unit of power (1 W = 1 J/s)
• pascal (Pa), the unit of pressure (1 Pa = 1 N/m²)
• hertz (Hz), the unit of frequency (waves or cycles per second)
• coulomb (C), the unit of charge
• volt (V), the unit of potential difference
• ohm (Ω), the unit of resistance

A prefix changes the size of a unit by a power of ten:

• nano (n) = 10⁻⁹
• micro (µ) = 10⁻⁶
• milli (m) = 10⁻³
• kilo (k) = 10³
• mega (M) = 10⁶
• giga (G) = 10⁹

To convert to a smaller unit, multiply. To convert to a bigger unit, divide.

Worked example: 2.5 kg in grams. 1 kg = 1000 g, so 2.5 × 1000 = 2500 g. And 24 000 mm in metres: 1 m = 1000 mm, so 24 000 ÷ 1000 = 24 m.

Choose the instrument that fits the quantity and the size of the measurement:

• ruler for length (a metre rule or 30 cm ruler)
• measuring cylinder for the volume of a liquid (more precise than a beaker)
• balance for mass
• stopwatch for time
• thermometer for temperature

When reading a scale, look at the smallest division and read to that division. Keep your eye level with the mark, and read a liquid at the bottom of its curved surface (the meniscus). Looking from an angle causes parallax error.

Accuracy means how close a result is to the true value. Precision means how close repeated readings are to each other.

Two types of error affect results:

• Random error: readings vary unpredictably, some too high and some too low (for example, reaction time with a stopwatch). Repeating and averaging reduces it.
• Systematic error: every reading is out by the same amount in the same direction (for example, a balance that reads 0.2 g with nothing on it, a zero error). Repeating does not remove it. You must find and correct the cause.

Taking repeat readings shows how reliable your results are and lets you spot an anomalous result (one that does not fit the pattern). Ignore anomalies when you calculate the mean.

Mean = total of readings ÷ number of readings

Worked example: readings of 12.1 s, 12.3 s and 12.2 s give a mean of 36.6 ÷ 3 = 12.2 s. The range (12.1 to 12.3 s) shows the spread.

Record results in a table with a heading and unit for every column (for example, Mass (g)), and the same number of decimal places for each column.

When plotting a graph:

• put the independent variable on the x-axis and the dependent variable on the y-axis
• label both axes with units and use a sensible scale
• plot each point accurately
• draw a line of best fit: a smooth line or straight line passing close to as many points as possible, with points above and below it. Do not join the dots.