Module One

MOTION

Introduction

This module should be read in conjunction with the Programme of Study.

The Programme of Study lists the topics that are in the module and gives you the relevant page references for your textbook. This module aims to give you more direction as you work through the various topics. It will aim to highlight the most important items in the topic, as well as areas that need particular care. It will also point you towards the resources you should be using.

Remember to double-check the syllabus to make sure you cover all the items that you need to.

Module Overview

In this module you will review how we express measurements in appropriate units, and how to calculate how things move, and push or pull each other. You need to build strong skills to analyse situations very logically, taking time to consider each situation clearly and carefully. This will make solving and calculating easy and reliable. Using simple diagrams really helps with this.

The equations of motion in this chapter apply only to uniform acceleration – that is constant acceleration in one direction. Remember that displacement, velocity and acceleration are vectors and this matters even for motion in a straight line, as we must use positive and negative numbers, the usual convention being that quantities pointing to the right are positive, and those to the left are negative, while for vertical motion upwards is positive and downwards is negative.

For projectile motion, we use the same equations, but for horizontal and vertical motion separately. Never mix up horizontal and vertical quantities in the same equation.

Pay particular attention to these key aspects:

• For kinematics (the equations relating displacement, initial and final velocity, acceleration, and time), take time to find the equation that gives the thing you need directly in one step, based on the things you know.
• With Newton’s laws (predicting how all things move) remember it is the resultant force that causes acceleration. Remember that forces always exist in pairs and recall the nature of those pairs: same size and type of force, but different objects and opposite directions, e.g. you push on the wall, the wall pushes on you in the opposite direction.
• Take time to become clear and reliable in drawing ‘free body force diagrams’ (showing all forces acting on one object) – these diagrams help avoid confusion and errors solving force problems. Remember if the system is in equilibrium, all the forces drawn ‘nose to tail’ of the arrow in the correct orientation (angle) will form a closed polygon.
• Thoroughly learn the rules of adding vectors, and how you can resolve them into 90° components that can be dealt with independently.

Maths required for this module

You will need to:

• Be extra cautious handling numbers, including rounding to correct significant figures, and expressing in Standard Form. Remember to carry forward all decimal places to subsequent calculations, not the rounded number.
• Understand and be aware of different base and derived units.
• Be able to estimate results, e.g. roughly how much something will change.
• Use estimates to check if calculation results are reasonable. For example, if the velocity is calculated to exceed the speed of light ($\color{blue}3.0\times10^8\ ms^{-1}$ ) then something has gone wrong.
• Rearrange equations.
• Substitute numerical values in algebraic equations.
• Plot graphs from data.
• Understand the meaning and significance of $\color{blue}y = mx + c$, as a linear relationship between variables $\color{blue}x$ and $\color{blue}y$.
• Determine the gradient and intercept of the line and recognise their physical meaning.
• Estimate the area between a graph and the $\color{blue}x$-axis.
• Recognise the physical significance of that area, e.g. in a speed-time graph.
• Use Pythagoras’ theorem, and the angle sum of the triangle (e.g. finding a resultant vector).
• Using sin, cos and tan in physical problems (e.g. resolving vectors and tangent ratios).
• Solve simple 2D geometry problems, like the sum of angles in a triangle.
• Draw and interpret scale drawings.

Topics

Topic One (1.1): Base and Derived Units, Estimation

Topic Two (1.2): Velocity and Acceleration

Topic Three (1.3): Motion Graphs

Topic Four (1.4): Adding Forces

Topic Five (1.5): Moments

Topic Six (1.6): Newton’s Laws of Motion

Topic Seven (1.7): Kinematics Equations

Topic Eight (1.8): Resolving Vectors

Topic Nine (1.9): Projectiles