**Disclaimer: **Due to unforeseen difficulties, we have had to take down the images on this notes page. They will be replaced shortly. We apologise for the inconvenience, but hope that the new images will provide you with an even better learning experience.

**Use and describe the use of rules and measuring cylinders to find a length or a volume**

To be honest, if you’re preparing for your IGCSEs, you should really know how to use a ruler, but I’ll explain it anyway.

A ruler is a flat object, usually rectangular, with markings along one or more of its straight edges.

These markings show us how long something is. It can only be used to measure other straight lines. If you want to measure something, hold the ruler against it, aligning the start of the edge of the object with the 0 on the ruler, and read off the ruler how long it is.

So in the image, the pen is 8.5cm long.

You can also use a ruler to measure the volume of regular shapes:

The volume of a cube or cuboid can be calculated by the formula height x length x width (V = hlw). Therefore, by using a ruler to measure the height, length and width of the cube or cuboid, we can calculate its volume.

Similarly, the volume of any pyramid or cone is equal to 1/3 x base area x height.

A measuring cylinder is used to measure the volume of a fluid. By filling the measuring cylinder with the fluid in question, we read off the marking that aligns with the lower meniscus of the fluid.

When you put liquid in a tube, you’ll notice that the upper surface of the liquid is curved – this curved surface is called the meniscus. The lower meniscus is the lowest part of that surface.

For example, in the image shown left, the lower meniscus lines up with the marking that denotes 43 ml, so we know that there is 43 ml of fluid in that measuring cylinder.

The method for measuring gas with a measuring cylinder is a little bit more complicated:

In this diagram, there is a reaction occurring in the conical flask between an acid and magnesium. This reaction gives off hydrogen gas.

Before the reaction begins, you set up the apparatus so that the water fills the measuring cylinder. As gas is produced from the reaction, it is fed through the delivery tube and come out the other end. Since gas is lighter than water, it goes up and gets trapped at in the cylinder, pushing the water out. You can then directly read the volume of gas produced off of the cylinder.

We can also use measuring cylinders to measure the volume of irregular objects using the water displacement method. The water displacement method, however, only works for objects that don’t react with water, don’t dissolve in it, and don’t absorb water.

There are two ways to do this. The first way only works if the object can fit inside the cylinder, and the second can be used if it doesn’t.

The first way:

You pour in a known volume of water into the cylinder and record its volume, e.g. you pour in exactly 15ml water.

You then carefully lower the irregular object into the cylinder, being careful not to splash any water.

Record the new volume reading. This total volume is the volume of the water + the volume of the object.

To get the volume of the object, we have to calculate total volume – volume of water, so calculate the difference between the two readings. This is the volume of the object.

The second way:

You fill a displacement beaker until full (the point where if you add any more water, it will pour out of the beaker). Then position a measuring cylinder at the spout of the beaker, so that it can collect all the water that pours out. Slowly lower the object into the beaker, being careful not to splash any water. The volume of water displaced into the measuring cylinder is equal to the volume of the object, so directly read off the volume of water in the cylinder.

Remember, 1 ml = 1 cm^{3} and 1 l = 1 dm^{3}.

**Understand that a micrometer screw gauge is used to measure very small distances.**

The image above shows a micrometer screw gauge. They are used to measure very small distances. The syllabus doesn’t tell you to know how to use a micrometer screw gauge, but I’m going to explain anyway, just in case. If you don’t think it’s necessary, skip over to point 3.

The device essentially measures the distance between the anvil and spindle, so you place an object between the two and adjust the position of the spindle by turning the thimble. The main scale shows graduations of mm, and the Vernier scale shows graduations of one-hundredth of an mm/ 10 μm. ‘μm’ is the symbol for micrometer.

To measure the distance between anvil and spindle, you look at the closest **visible** marking to the thimble and write down the corresponding number. For example, in the above image, the closest visible marking is the 7^{th} one, so record the value as 7mm.

Next, look at the Vernier scale. The number on the Vernier scale that lines up with the middle line on the sleeve is the number that has to be recorded. In the image above, that number is 37. Since the Vernier scale graduates by 10 μm each time, we know that this is actually 37 x 10 = 370 μm.

You then add these two readings together to find the distance between anvil and spindle.

So distance = 7mm + 370 μm

1 mm = 1000 μm, so distance = 7mm + 0.37mm = 7.37mm

Or distance = 7000 μm + 370 μm = 7370 μm.

**Use and describe the use of clocks and devices, both analogue and digital, for measuring an interval of time**

I really don’t think I need to explain how a clock works and how you read it.

You guys should know how to use timers too. If you don’t, drop a comment and I’ll update the notes to include an explanation.

If you’re using a clock to measure the length of a time interval, measure the time at the start of the interval (ie. when t = 0) and measure the time at the end of the interval. Then find the difference.

If using a stopwatch, start the stopwatch at the beginning of the time interval and stop it at the end. Then directly read off the time that has lapsed over the course of the interval.

** **

**Obtain an average value for a small distance and for a short interval of time by measuring multiples (including the period of a pendulum)**

Whenever you take a measurement, it is always a good idea to take multiple of the same measurement and find the mean, as it reduces any inaccuracies.

For example, if you were attempting to measure the diameter of a circle with a ruler, measure the diameter as accurately as you can at least three times from different angles. Then find the mean. This is the value that should be used in any further calculations.

Same thing for time – if you are measuring how long it takes for a reaction to finish, for example, repeat the reaction multiple times and calculate the mean.

If you’re trying to measure the period of a pendulum, however, the method to find the mean time is slightly different.

First let me explain some basic terms, in case you don’t know much about pendulums.

A pendulum is a mass that swings back and forth about a fixed point.

One single oscillation of a pendulum is when it swings back to the exact same position and achieves the same state of motion that it started at.

For example, if the pendulum started swinging from its right most point (from its position of maximum amplitude), the mass would have to swing towards the left and then come back all the way to the right to complete one oscillation.

If the start point is the middle, it would have to swing all the way in one direction, all the way in the other direction, and then back to the middle to complete one oscillation.

The time taken to complete a single oscillation is called a period.

To measure the period of a pendulum, you usually measure the time taken for **ten oscillations **and then **calculate the mean**. That is, you divide the total length of time by 10, to get the period of one oscillation. This will reduce the error in measurement as human reflexes are usually too slow to be completely accurate, and that inaccuracy can have a major impact on something as small as a period.

But yeah, as a general rule, calculating the average makes your measurements a lot more reliable!

*Notes submitted by Sarah.*

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