What is a physical quantity?
A physical quantity is a property we can measure. We write it as a number and a unit, for example 6 cm, 5 N or 36 km/h. Without the unit the number means nothing. To measure we need an instrument: a ruler, a balance, a stopwatch, a thermometer. We use the SI units (metre, kilogram, second) because they are the same all over the world.
Speed, volume and weight
Speed tells how fast something moves: speed = distance ÷ time. Units: m/s or km/h. 36 km/h is 10 m/s.
Volume is the space an object takes up. For a box, V = length × width × height. Units: cm³ or m³. For liquids we use litres: 1 litre = 1000 cm³.
Mass is how much matter is in an object (kg, g). Weight is the pull of the Earth on that mass. It is a force, measured in newtons (N): W = m × g, with g about 10 N per kg. A 5 kg bag weighs about 50 N. Mass stays the same on the Moon. Weight becomes about one sixth.
A force is a push or a pull. It can change speed, direction or shape.
Density and floating
Density tells how much mass is packed in each cm³: density = mass ÷ volume. Units: g/cm³ or kg/m³. Water is 1 g/cm³ (1000 kg/m³). Wood is about 0.6, ice about 0.9, aluminium 2.7 and iron 7.9 g/cm³.
Floating: an object floats if its density is less than the liquid. It sinks if its density is more. A floating object sits partly under water. For density 0.6 about 60% of the object is under water. A steel ship floats because its hollow shape holds a lot of air, so the whole ship (steel plus air) is less dense than water.
Pressure
Pressure is how strongly a force presses on each unit of area: pressure = force ÷ area. The unit is the pascal (Pa): 1 Pa = 1 N on 1 m². The same force on a smaller area gives more pressure. That is why a knife is sharp, a nail has a point, and a camel has wide feet for sand.
Liquids also press. Pressure grows with depth, which is why a dam wall is thicker at the bottom. In communicating vessels (pots joined by a pipe at the bottom) the same liquid reaches the same level in every pot, whatever the shape.
Temperature, heat and electric charge
Temperature tells how hot or cold something is. We measure it with a thermometer in °C. It shows how fast the tiny particles move.
Heat is energy that flows from a hotter object to a colder one (measured in joules). A big pot of warm water holds more heat than a spoon of boiling water, though the spoon has a higher temperature. So heat and temperature are different.
Electric charge (unit: coulomb) is a property of matter. Charges are positive or negative. Like charges push each other away, unlike charges pull together. Moving charges make an electric current.
In a simple circuit we join a battery, a switch and a bulb in one closed loop with wires. When the switch is closed, charges flow and the bulb glows. If the loop is open, nothing flows.
Three classic experiments
- Inclined plane (ramp): lifting a load up a ramp needs less force than lifting it straight up, but you push over a longer distance.
- Floating: try wood, a stone, a coin and a plastic bottle in a bucket. Predict first, then check using density.
- Communicating vessels: pour water in one of two connected bottles of different shapes. The water rises to the same level in both.
Try it
At home: Put a cork, a coin, an apple and a plastic spoon in a basin of water. Guess which float and which sink. Then check. Press a pencil on your palm with the tip, then with the flat end. Which feels sharper? That is pressure.
In the 3D: Before dipping, guess whether wood, ice, aluminium or iron will float. Then dip each one.
Key formulas and definitions
- speed = distance ÷ time
- V = l × w × h (box)
- W = m × g (g ≈ 10 N/kg)
- density ρ = mass ÷ volume
- pressure P = force ÷ area (1 Pa = 1 N/m²)
- floats if ρ(object) < ρ(liquid)
- Units: m/s, cm³, N, g/cm³, Pa, °C, J, C
Worked examples
1. A car travels 150 km in 3 hours. Find its speed.
Speed = distance ÷ time = 150 ÷ 3 = 50 km/h.
2. A box is 5 cm long, 4 cm wide and 3 cm high. Find its volume.
V = 5 × 4 × 3 = 60 cm³.
3. A bag has a mass of 5 kg. Find its weight. (g = 10 N/kg)
W = m × g = 5 × 10 = 50 N.
4. A piece of aluminium has mass 270 g and volume 100 cm³. Find its density.
Density = 270 ÷ 100 = 2.7 g/cm³.
5. A force of 600 N presses on an area of 0.03 m². Find the pressure.
P = F ÷ A = 600 ÷ 0.03 = 20 000 Pa.
6. A block has mass 200 g and volume 250 cm³. Does it float in water? How much of it is under water?
Density = 200 ÷ 250 = 0.8 g/cm³, which is less than 1, so it floats. About 0.8 = 80% of it is under water.
7. An iron cube has sides 5 cm. Iron density is 7.9 g/cm³. Find its mass and weight. (g = 10 N/kg)
V = 5 × 5 × 5 = 125 cm³. Mass = 7.9 × 125 = 987.5 g = 0.9875 kg. Weight = 0.9875 × 10 ≈ 9.9 N.
Common mistakes
- Mixing up mass and weight. Mass is in kg and stays the same everywhere. Weight is a force in newtons.
- Thinking heat and temperature are the same. Temperature tells hot or cold; heat is the energy that flows.
- Saying a heavy object always sinks. What matters is density, not total weight. A huge log floats.
- Forgetting units, or using cm² with m²: change them to the same unit before dividing.