make reasonable estimates of physical quantities included within the syllabus

What is a Physical Quantity?

A physical quantity is something we can measure, like length, mass or time. It has a value and a unit. Think of it as a number that tells you how much of something there is.

SI Base Units

Derived Units

Derived units are made by combining base units. For example, speed is length divided by time:

$v = \frac{l}{t}$

So the unit of speed is metres per second (m/s).

Order of Magnitude

When you’re unsure, estimate how many powers of ten a quantity is close to. For example, the mass of a human is roughly $70\,\text{kg} \approx 10^2\,\text{kg}$.

Tip: Write the number in scientific notation and drop the decimal part.

Dimensional Analysis

Use the dimensions of the quantities you know to deduce the dimensions of an unknown. For example, the period of a simple pendulum depends on its length $l$ and the acceleration due to gravity $g$:

$$T \propto \sqrt{\frac{l}{g}}$$

Check that both sides have the same dimensions: $[T] = \sqrt{[L]/[LT^{-2}]} = T$.

Significant Figures & Rounding

When you estimate, keep 1–2 significant figures. For example, the speed of light $c = 3.0 \times 10^8\,\text{m/s}$ is usually written with two significant figures.

Rule: If you’re not sure, round to the nearest power of ten.

Mass of a Tennis Ball

Typical tennis ball radius ≈ 3.5 cm = 0.035 m. Volume ≈ $\frac{4}{3}\pi r^3$ ≈ $1.8 \times 10^{-4}\,\text{m}^3$. Density of rubber ≈ $1100\,\text{kg/m}^3$. Mass ≈ $0.2\,\text{kg}$.

Real value ≈ 0.057 kg – you got close enough for a rough estimate!

Weight of a 70 kg Person on the Moon

Moon’s gravity ≈ $1.6\,\text{m/s}^2$ vs Earth’s $9.8\,\text{m/s}^2$. Weight scales linearly with gravity.

$$W_{\text{moon}} = W_{\text{earth}} \times \frac{1.6}{9.8} \approx 70\,\text{kg} \times 0.16 \approx 11\,\text{kg}$$

So you’d feel like you weigh only about 11 kg on the Moon.

Tip 1: Check Units Early

Before you do any calculation, write down the units of each quantity. If the final units don’t match the required answer, you’ve made a mistake.

Tip 2: Use Order of Magnitude for Quick Checks

After solving, compare your answer’s magnitude with a rough estimate. If it’s off by more than an order of magnitude, double‑check your work.

Tip 3: Keep Significant Figures in Mind

When the problem states “give your answer to two significant figures”, round accordingly. Don’t over‑specify.

• Physical quantities have a value and a unit.
• Use SI base units and derived units correctly.
• Estimate using order of magnitude, dimensional analysis, and significant figures.
• Always check units and magnitudes before finalising your answer.

Remember: Estimation is a powerful tool that helps you spot errors and understand physics intuitively. Happy estimating! 🚀