Lesson Notes By Weeks and Term v4 - SHS 2

Lesson Video

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Performance objectives

• Define key terms related to physical quantities.
• Establish proportional relationships between variables.
• Use dimensional analysis to check the validity of equations.
• Solve problems to find relationships between quantities.
• Apply these concepts to real-life scenarios.

Lesson summary

In our last lesson, we learned how to check if a physics equation is correct using the dimensions of the quantities involved. Today, we will take this powerful skill a step further. We will learn how physicists can actually *derive* or create a formula from scratch, just by knowing which physical quantities are related to each other. This method, called dimensional analysis, is like being a detective for the laws of nature. It helps engineers design safe bridges in Accra, scientists at the Noguchi Memorial Institute understand fluid dynamics, and even helps us understand why a pendulum swings the way it does. It is a fundamental tool for thinking like a scientist.

Lesson notes

Recap: The Foundation - Principle of Homogeneity

Before we build, we must check our foundation. Remember the Principle of Homogeneity of Dimensions: a physically correct equation must have the same dimensions on both the left-hand side (LHS) and the right-hand side (RHS). For example, in the equation `Force = mass × acceleration` (`F = ma`): Dimensions of LHS (Force): [F] = [M L T⁻²] Dimensions of RHS (ma): [m][a] = [M] × [L T⁻²] = [M L T⁻²] Since LHS = RHS, the equation is dimensionally consistent. We will use this exact principle to build new equations. The Core Skill: Deriving Relationships Between Physical Quantities

Imagine you observe a phenomenon and you have a hypothesis about what factors influence it. For example, you notice that the time it takes for a pendulum to complete one swing (its period, *T*) seems to depend on its length (*l*) and maybe the acceleration due to gravity (*g*). But what is the exact formula? Is it `T = l × g`? Or `T = l²/g`? Dimensional analysis helps us find out.

We will follow a clear, step-by-step method:

Evaluation guide

• Establish the relationship between quantities .
• Talk for Learning: Set up proportionalities between dependent variable and independent
• variables and use the dimensions of the quantities and simultaneous equations to establish the
• degree of dependency and subsequently establish the relationship between quantities.