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# Measuring quantities

## Measuring lengths with a ruler

To measure the length of everyday objects we normally use a ruler or a tape measure.

The length of a pencil is measured using a ruler to be $8.9 \ucm.$

Rulers and tape measures can measure an object to within $1 \umm$.

• The object being measured must be straight and laid next to the ruler or tape measure.
• The object must be exactly in line with the zero on the ruler or tape measure.
• Repeating the measurement a number of times and taking the average will make the result more precise.
The object being measured is very close to the ruler and is exactly in line with the zero mark.

## Measuring lengths with vernier callipers

Vernier calipers are used to measure small distances. They are used when a ruler or tape measure is not precise enough. Vernier calipers can measure to the nearest $0.1 \umm$.

Vernier calipers can be used to measure the diameter of a coin.

To measure something using vernier calipers:

1. Place the object inside the jaws. Tighten the jaws until they are firmly against the object.
2. Read the last main scale marking before the zero on the vernier scale. This is the length in millimetres.
3. Look at the vernier scale. Find the point where one of the markings on the vernier scale matches one of the points on the main scale. This is the number of tenths of a millimeter that must be added to the main scale reading.

The scale below shows $\Tred{17 \umm} + \Tblue{0.6 \umm} = 17.6 \umm$

## Measuring lengths with micrometers

Micrometers are used to measure very small thicknesses and lengths. They are used when vernier calipers are not reliable enough. Micrometers can measure to the nearest $0.01 \umm$.

Micrometers can be used to measure the thickness of a wire.

To measure something using a micrometer:

1. Place the object inside the jaws. Turn the screw until the object is firmly secured..
2. The divisions in the main scale are $0.5 \umm$. Read the main scale to the nearest $0.5 \umm$.
3. Read the additional fraction of a millimetre from the fractional scale.

The micrometer below is reading $\Tred{5.5 \umm} + \Tblue{0.26 \umm} = 5.76 \umm$

## Measuring the period of a simple pendulum

The period of a simple pendulum is the time taken for the pendulum to complete one full cycle. Its SI unit is the second.

One full cycle begins when the pendulum passes the equilibrium position, b and ends when the pendulum passes the same point again travelling in the same direction.

To measure the period of a simple pendulum, set the pendulum in motion and wait until it starts swinging steadily.

Start the stopwatch as the pendulum passes the equilibrium position. Stop the stopwatch after the pendulum has completed at least ten cycles. Only stop the pendulum after a whole number of cycles.

The period of the pendulum is calculated using $$\text{period}= \frac{\Tblue{\text{time taken}}}{\Tred{\text{number of full cycles}}}$$

If the pendulum takes $\Tblue{\text{18.6}}$ to complete $\Tred{\text{20}}$ full cycles the period is $$\frac{\Tblue{\text{18.6}}}{\Tred{\text{20}}} = 0.93 \us$$

The pendulum swings between a and c. b is the position of the pendulum when it is not swinging.