Rectilinear Motion

Rectilinear motion is simply movement along a straight line - think of a car driving down a motorway or a ball rolling across the floor. The maths behind this is surprisingly manageable once you get the hang of it.

Average velocity equals displacement divided by time (Δx/Δt), whilst acceleration measures how quickly velocity changes over time (Δv/Δt). Remember that both velocity and acceleration are vectors, so direction matters - if something slows down, it has negative acceleration.

Free fall happens when objects drop without air resistance, and here's the brilliant bit: everything falls at exactly the same rate of 9.81 ms⁻², whether it's a feather or a bowling ball. Gravity always pulls downward, so if you throw something upward (positive velocity), gravity gives it negative acceleration.

Quick tip: For projectile motion, treat horizontal and vertical movements separately - horizontal velocity stays constant whilst vertical motion accelerates downward at 9.8 ms⁻².

Motion Graphs and Momentum

Displacement-time graphs show you the story of an object's journey - the gradient tells you the velocity. A straight line means constant velocity, whilst a curve indicates acceleration. It's like reading a travel diary in graph form.

Velocity-time graphs are equally revealing. The gradient gives you acceleration, and the area under the line equals displacement. These graphs turn complex motion into visual stories you can actually understand.

Momentum equals mass times velocity, and it follows one of physics' most important rules: the principle of conservation of momentum. In any collision or interaction, the total momentum stays the same (assuming no external forces interfere). This principle explains everything from snooker shots to car crashes.

Remember: The area under any velocity-time graph always gives you the displacement - this comes up constantly in exam questions!

Newton's Laws and Forces

Newton's three laws govern everything that moves around you. The first law says objects keep doing what they're already doing unless something forces them to change - your shopping trolley rolls straight until you steer it.

Newton's second law connects force, mass, and acceleration $F=ma$, whilst also defining impulse as force multiplied by time, which equals the change in momentum. This explains why airbags work - they increase the time of impact, reducing the force on your body.

The third law states that every action creates an equal and opposite reaction. When you walk, you push backward on the ground, and it pushes you forward with equal force. These force pairs always act on different objects and along the same line.

Weight $W=mg$ is the gravitational force pulling you toward Earth. When forces balance out completely, objects reach equilibrium - like a book resting on a table.

Key insight: Third law force pairs must act on separate bodies - a common exam trick is showing forces on the same object and asking if they're a third law pair!

Moments and Work

Moments measure the turning effect of forces - think of using a spanner or opening a door. The moment equals force times perpendicular distance from the pivot point. Longer spanners make jobs easier because they increase this distance.

The principle of moments keeps things balanced: clockwise moments must equal anticlockwise moments for equilibrium. This principle explains why playground seesaws work and how cranes don't topple over.

Work done equals force times distance moved in the direction of that force. Since force and displacement are vectors but work is a scalar, direction matters for the calculation but not for the final answer.

Energy is simply the ability to do work. Potential energy comes from position or state - a book on a high shelf has gravitational potential energy, whilst a stretched elastic band has elastic potential energy.

Practical tip: To increase a moment (turning effect), you can either increase the force or increase the distance from the pivot - this is why door handles are placed far from hinges!

Energy Types and Transformations

Kinetic energy (KE = ½mv²) belongs to moving objects - the faster something moves, the more energy it carries. When speed changes from u to v, the change in kinetic energy equals ½mv² - ½mu².

Gravitational potential energy (GPE = mgh) increases with height above a reference point. A classic example is a pendulum, which constantly converts between kinetic and potential energy as it swings. At the highest points, GPE is maximum and KE is zero; at the bottom, it's the opposite.

Real pendulums gradually lose energy to air resistance and friction, causing the amplitude to decrease. This "lost" energy doesn't disappear - it becomes internal energy, increasing the temperature of the pendulum and surrounding air.

Energy exists in many forms: chemical energy in food and fuel, nuclear energy in atomic reactions, and others. The beauty is that energy can transform between these forms but never gets created or destroyed.

Energy insight: When solving energy problems, always identify what type of energy you start with and what type you end with - the total amount stays constant!

Conservation and Efficiency

The principle of conservation of energy is one of physics' most fundamental rules: energy cannot be created or destroyed, only transferred from one form to another. This principle helps you solve complex problems by tracking energy transformations.

Efficiency measures how well energy conversion processes work, calculated as useful energy output divided by total energy input, multiplied by 100%. No real process is 100% efficient - some energy always becomes heat.

Power tells you the rate of energy transfer or work done, measured in watts. A 100W light bulb transfers 100 joules of electrical energy per second into light and heat.

Understanding these concepts helps you analyse everything from car engines to renewable energy systems. The maths might look intimidating initially, but these principles describe the physical world in remarkably elegant ways.

Efficiency reality check: If a question gives you 100% efficiency, double-check your working - real-world processes always lose some energy as heat due to friction or resistance!