Revise Physical quantities for Cambridge 9702 (1.1)

A physical quantity isn't just a number; it's a number paired with a specific unit. For instance, '5 metres' means a length of five units, where each unit is a metre. This standardised approach ensures everyone understands the same measurement, no matter where they are in the world.

Derived units, on the other hand, are formed by combining these base units. They allow us to express more complex quantities like speed, force, or energy using the fundamental building blocks.

For example, the unit for force, the Newton (N), is equivalent to kg m s⁻².

To handle very large or very small measurements, we use SI prefixes. These are multipliers that simplify writing numbers. Instead of writing 1,000,000 metres, we can simply say 1 Megametre.

A crucial concept for equation validity is dimensional homogeneity. This means that the units on both sides of any correct physical equation must match. It's a powerful tool to check your calculations!

Not all quantities are the same; some only need a value, while others also require a direction. This distinction separates scalars from vectors. Understanding this difference is fundamental to describing motion and forces accurately.

When adding vectors, you must account for their directions. For two perpendicular vectors, like forces acting at right angles, we use Pythagoras' theorem for the resultant magnitude and trigonometry for its direction.

For perpendicular vectors $A$ and $B$, resultant magnitude $R = \sqrt{A^2 + B^2}$. Direction $\theta = \text{arctan}(\frac{B}{A})$.

For non-perpendicular vectors, the easiest way to add them is by resolving them into perpendicular components. Each vector is broken down into its 'x' and 'y' parts, which can then be added independently.

A vector $V$ making an angle $\theta$ with the x-axis can be resolved into components: $V_x = V \cos \theta$ and $V_y = V \sin \theta$.

In experimental physics, our measurements are never perfect. We need to understand the limitations of our instruments and methods. This involves distinguishing between accuracy, precision, and recognising different types of errors.

Random errors are unpredictable variations that cause results to spread around the true value. They arise from factors like fluctuating conditions or human reaction times.

Systematic errors cause all readings to consistently deviate from the true value in the same direction. They often stem from faulty equipment or flaws in the experimental design.

Uncertainty is the estimated range within which the true value of a measurement is expected to lie. It's crucial to express this range to reflect the reliability of your data. For a single reading, the absolute uncertainty is typically $\pm half the smallest division on the instrument$. For a difference (e.g., length measured between two points), it's $\pm one smallest division$.

When you use multiple measurements to calculate a final result, their individual uncertainties must be combined appropriately to determine the overall uncertainty of the final value. Different rules apply depending on the mathematical operation.