Exploring Diversity of Matter by Its Physical Properties

• Base quantities are the fundamental quantities from which all others are built. There are seven base quantities in the SI system.
• Derived quantities are physical quantities that are derived from base quantities. For example, speed is derived from the two base quantities of distance and time: speed = distance ÷ time.

The International System of Units (SI) was established in 1968 and is used by most countries today. All derived quantities can be expressed in terms of these seven base quantities.

When measuring quantities that are either very large or very small, it can become difficult to write down their numerical magnitude. In standard form, a number is denoted as a × 10ⁿ, where 1 ≤ a < 10 and n is an integer.

• 5 700 000 = 5.7 × 10⁶
• 0.045 = 4.5 × 10⁻²
• 3600 = 3.6 × 10³

Prefixes are abbreviations that represent certain powers of 10. Write the prefix directly in front of the unit with no space — for example, 1 × 10³ m may be written as 1 km.

Instruments have a limited degree of precision (e.g. a ruler measures only to 0.1 cm), so calculated results also have limited precision. The number of digits known with some reliability is the number of significant figures (s.f.). For example, if a calculation gives "8.910243 kg" but the measurements are precise only to the hundredths digit, write 8.91 kg (3 s.f.).

The precision of a calculated result is limited by the least precise measurement involved.

• Addition & subtraction: round to the same number of decimal places (d.p.) as the measurement with the fewest d.p. — e.g. 300.0 (1 d.p.) + 13.643 (3 d.p.) = 313.643 → 313.6 (1 d.p.).
• Multiplication & division: round to the same number of s.f. as the component with the fewest s.f. — e.g. 3.0 (2 s.f.) × 12.60 (4 s.f.) = 37.8 → 38 (2 s.f.).
• Logarithmic operations: the result must have the same number of s.f. as the input — e.g. lg[0.943 (3 s.f.)] = −0.025 (3 s.f.).

• Occur in all measurements. They arise when observers estimate the last figure of a reading, or due to background noise and mechanical vibrations.
• They are of different signs and magnitude.
• Best minimised by taking a large number of readings and finding their average.

• Cause consistent underestimating or overestimating of a reading.
• Arise from faults in the equipment (e.g. zero error) or environmental factors that remain constant throughout the measurement (e.g. certain weather conditions).
• They are of the same sign and magnitude under the same conditions, and can only be eliminated if the sources of error are known.

• Zero error (a type of systematic error): when the instrument does not read zero with nothing on it. On electronic instruments, use the "tare" function to reset the scale.
• Parallax error: occurs when a marking is viewed from the wrong angle. When reading off a scale, position your eye so that the line of sight is perpendicular to the scale. Viewing from above or below gives readings that are too high or too low.

Imagine each dartboard as the true value of a quantity, and each black dot as a reading.

• The more accurate a reading, the closer it is to the true value (dot near the bull's-eye).
• The more precise the readings, the closer they are to one another.
• Inaccurate measurements can be caused by systematic errors; imprecise measurements can be caused by random errors.

• Precise to one hundredth of a centimetre, or 0.01 cm.
• Main scale + vernier scale; outside jaws (external diameter/length), inside jaws (internal diameter/length), and a tail (depth).

1. Note the reading on the main scale just before the zero mark on the vernier scale (e.g. 2.9 cm).
2. Find the vernier marking that lines up with a marking on the main scale, and read its value (e.g. 0.04 cm).
3. Add them: observed reading = 2.9 + 0.04 = 2.94 cm.

• Close the empty jaws. If "0" on both scales is exactly in line → no zero error.
• If not, note how far off they are (e.g. +0.02 cm or −0.01 cm).
• Corrected reading = observed reading − zero error.

• Precise to one hundredth of a millimetre, or 0.01 mm.
• Parts: anvil, spindle, sleeve (main/linear scale) with 1.0 mm and 0.5 mm divisions, circular scale on the thimble (50 divisions of 0.01 mm each), ratchet, frame and lock lever.

1. Clamp the object between the anvil and spindle. Turn the ratchet until it slips and a "tick" sound is heard.
2. Note the reading on the main scale (e.g. 6.5 mm).
3. Note the circular-scale marking in line with the centre line of the main scale (e.g. 0.35 mm).
4. Add them: observed reading = 6.5 + 0.35 = 6.85 mm.

• Turn the ratchet until the spindle touches the anvil. If "0" on both scales coincides → no zero error.
• Corrected reading = observed reading − zero error.
• Precaution 1: do not tighten the thimble too much — over-tightening can damage the screw.
• Precaution 2: dirt on the anvil or spindle affects the reading — clean both before each measurement.

The SI unit for area is the metre squared (m²); other common units are cm², mm² and km². For regular shapes, measure one or more dimensions and apply a formula:

• Place the shape on a grid and count squares. General rule: mark "1" in a box only if more than 50% of it is occupied.
• Worked example (flower outline, 0.50 cm squares): total squares = 58; area of one square = 0.50 × 0.50 = 0.25 cm²; area = 58 × 0.25 = 14.5 cm² ≈ 15 cm² (2 s.f.).

Instruments read once per measurement (e.g. measuring cylinders, thermometers — read at the liquid meniscus): estimate to half the smallest division.

• A 100 mL measuring cylinder has a smallest division of 1 mL → record readings to 0.5 mL (one decimal place; last digit is "0" or "5").
• E.g. a reading of 52.0 mL actually represents the range 51.5–52.5 mL, written as (52.0 ± 0.5) mL.

Instruments read twice per measurement (e.g. metre rules, protractors — the difference between two readings is the measurement): record to the smallest division itself, since the overall uncertainty doubles.

• E.g. a length measured as 1.1 cm represents the range 1.0–1.2 cm, written as (1.1 ± 0.1) cm.

• A scalar is a physical quantity that has only magnitude.
• A vector is a physical quantity that has both magnitude and direction.

The sum of two vectors is the resultant. Both magnitude and direction must be considered.

• Same direction: |F| = F₁ + F₂ — the arithmetic sum, in the same direction as both forces.
• Opposite directions: |F'| = |F₁ − F₂| — the difference, in the direction of the greater force.

The SI unit for volume is the cubic metre (m³). In practice, litres (L) and millilitres (mL) are used for fluids, while cm³ and mm³ are used for solids. It would be inappropriate to describe a solid's volume in litres.

1. Partially fill the cylinder with water and note the level (e.g. 50 mL).
2. Place the object in, ensuring no water overflows and the object is completely covered. Note the new level (e.g. 58 mL).
3. Volume of object = new level − original level = 58 − 50 = 8 mL.

1. Tie the object to a string with a sinker (an object denser than water) on one end.
2. Lower only the sinker into the water (object still above the surface). Note the level (e.g. 58 mL).
3. Lower both until fully submerged. Note the new level (e.g. 66 mL).
4. Volume of object = new level − sinker-alone level = 66 − 58 = 8 mL.

• Fill the displacement can until water reaches the spout.
• Submerge the object (regular or irregular) — it displaces a volume of water equal to its own volume.
• The volume of displaced water collected = the volume of the object.

• A beam with a weighing pan suspended from each end; the beam should be horizontal when empty.
• Place the object on one pan, then add standard masses to the other until the beam is horizontal again.
• The total mass of the standard masses = the mass of the object.

• Precision varies: kitchen balances up to 1 g; laboratory analytical balances up to 0.0001 g.
• The reading should be zero before weighing — use the "tare" button if not.
• Tare also removes the container's mass: place an empty beaker on, press tare (reading → 0.00), then pour in the substance — the balance shows only the contents' mass (e.g. 0.50 kg).

• Note: the symbol ρ is the Greek letter "rho", not a letter "p".
• Conversion: 1 g cm⁻³ = 1000 kg m⁻³.

An alloy is created from aluminium and copper in a factory.

• (a) Density of aluminium = 2700 kg m⁻³. If 8100 kg of aluminium is used, volume V = m ÷ ρ = 8100 ÷ 2700 = 3.0 m³.
• (b) 35 600 kg of copper occupies 4.0 m³. Density of copper = 35 600 ÷ 4.0 = 8900 kg m⁻³.
• (c) The alloy has density 6200 kg m⁻³. A block with volume 1.5 m³ has mass m = ρ × V = 6200 × 1.5 = 9300 kg.

A hydrometer measures the density of liquids. It floats upright (a weight at the bottom keeps it vertical) on a stem with a marked scale. The denser the liquid, the higher the hydrometer floats — compare the liquid level against the scale markings to infer the density.

• The SI unit for time is the second (s).
• Has a minute scale and a second scale; the smaller minute hand shows minutes, the bigger second hand shows seconds.
• Smallest division of 0.2 s → precise to two-tenths of a second (0.2 s). Example reading: 1 minute and 9.0 seconds.

• Digital display with greater precision — measures to one hundredth of a second, or 0.01 s.
• Steps: (1) press "reset" so the display reads 0:00.00; (2) press "start/stop" once to start; (3) press it again to stop at the required interval; (4) record the time in minutes and seconds (e.g. 2 min 5.82 s); (5) press "reset" for the next reading.

To measure a periodic event (e.g. pendulum oscillations) more precisely, record the time over many events and take the average.

For small angles of displacement, the period of a simple pendulum:

• increases when the pendulum length increases,
• decreases when the gravitational field strength increases,
• is independent of both the mass of the bob and the angle of displacement.

1. Set up the pendulum on a retort stand with string and bob.
2. Release it from an angle of ≤ 5° to the vertical.
3. Let it swing a few times before taking readings, so the oscillations stabilise.
4. Measure the time for 20 oscillations, t₁. Repeat for another 20 oscillations and record t₂.
5. Calculate the average time t for 20 oscillations, hence the period T = t ÷ 20 for one oscillation.

Rate is a measure of the change in one quantity with respect to another. Most rates involve change with respect to time, but not all:

• If an object floats in a medium, it is less dense than the medium (e.g. wood in water); if it sinks, it is denser (e.g. iron in water).
• Purity test: pure substances have a fixed density. A piece of gold suspected of being impure can be measured and compared against the density of pure gold.

Strength is the ability of a material to resist breaking, tearing, or changing its shape permanently. Pure metals are weak and can be made stronger by combining them with other elements to form alloys. For example, steel (an alloy of iron and carbon) is very strong.

• Hardness is the ability of a material to withstand scratches (surface abrasion).
• The Mohs hardness scale consists of 10 minerals given arbitrary hardness values: talc is the softest (1) and diamond the hardest (10).
• A material can scratch all materials softer than itself, but cannot scratch those harder.
• Diamond (a form of carbon) is extremely hard and can only be cut by other diamonds. Titanium, one of the hardest metals, is used in supersonic aircraft and artificial human bones.

Flexibility is the ability of a material to bend without breaking, and to return to its original size and shape after being bent. The greater the flexibility, the smaller the force needed to bend it by a certain amount.

• Electrical conductivity measures how easily a material allows electric current to flow through it.
• Electrical insulators do not allow electricity to flow through them easily. Plastics (insulators) are used to insulate electrical cables made of copper — a good conductor.
• Non-metals, with the exception of graphite (carbon), are good electrical insulators due to the absence of free electrons that act as mobile charge carriers.

• Thermal conductivity measures how easily a material allows thermal energy to flow through it.
• Thermal conductors: copper, silver, diamond and gold. Thermal insulators: plastics, fur and wood.
• Frying pans are made of metal (thermal conductor), while winter clothing is lined with fleece (thermal insulator).

• The melting point is the temperature at which a material changes from the solid state to the liquid state.
• Strong metallic bonds account for the high melting points of most metals — hence metals are used for cooking and baking tools (pots, frying pans, baking trays) that must not melt at high temperatures.
• Impurities lower the melting point and cause melting to occur over a wider range of temperatures. E.g. salt is thrown on icy roads in winter to lower ice's melting point so it melts, clearing the road.
• Purity test: like density, pure solids have a fixed melting point.

• The boiling point is the temperature at which a material changes from the liquid state to the gaseous state.
• Lowering atmospheric pressure lowers the boiling point — water boils below 100 °C at high altitudes. Conversely, increasing pressure raises it.
• Impurities increase the boiling point and cause boiling to occur over a wider range of temperatures.
• Purity test: pure liquids have a fixed boiling point.

• The x-axis represents the independent variable; the y-axis represents the dependent variable.
• Both axes must be labelled, including units for physical quantities.
• Title format: "Graph of y against x" — e.g. "Graph of distance / m against time / s".

• If points show an obvious curved trend, draw a smooth curve through them — do NOT connect the points with straight-line segments.
• For a linear relationship, draw a straight line of best fit with a ruler: points not on the line should be evenly distributed on both sides. The line passes through as many points as possible but need not pass through any particular point.