Mechanics Overview

You'll be diving into the core topics that make up mechanics - the study of motion and forces. This section covers everything from basic scalars and vectors to more complex ideas like momentum conservation and projectile motion.

The key areas include understanding forces, how objects accelerate, and the relationship between work, power, and energy. You'll also explore Newton's laws of motion and learn to interpret motion graphs.

Remember: Mechanics connects maths with real-world physics - once you grasp the fundamentals, everything else becomes much clearer!

Don't worry if it seems overwhelming at first. Each topic builds on the previous one, so take your time with the basics and you'll find the advanced concepts much easier to tackle.

Scalars & Vectors

Think of this as the difference between saying "I ran 5 kilometres" versus "I ran 5 kilometres north" - one gives you the full picture, the other doesn't. Scalars only tell you the size (magnitude) of something, like speed, time, or distance.

Vectors, on the other hand, give you both size and direction. Displacement, velocity, acceleration, and force are all vectors because knowing which way they point is crucial for solving problems.

When drawing scale diagrams, always use a ruler and protractor, and clearly state your scale ratio. For simple cases like "2 metres east + 3 metres west = 1 metre west," you can work it out in your head.

Top tip: If two vectors are perpendicular, use Pythagoras' theorem to find the resultant - it's your best friend in physics!

Vector Calculations

Here's where the maths gets practical. When you have perpendicular vectors, like a velocity of 14 m/s east combined with 8 m/s north, you're looking at a right-angled triangle problem.

Use Pythagoras' theorem: R = √(14² + 8²) = 16 m/s. Then find the angle using trigonometry: θ = tan⁻¹(8/14) = 30°. So your resultant is 16 m/s at a bearing of 30°.

For non-perpendicular vectors, you'll need to break them into components first. Use cosine for horizontal components and sine for vertical components, then apply Pythagoras to the total components.

Quick check: Always sketch the vectors first - it helps you visualise what's happening and catch silly mistakes!

Forces in Equilibrium

An object is in equilibrium when it's either stationary or moving at constant velocity. This happens when all forces balance out - the sum of forces equals zero, and the sum of all moments around any point also equals zero.

Free body diagrams are your roadmap for these problems. Draw the object and show every single force acting on it with arrows. For a car on flat ground, you'd show gravity pulling down, the road pushing up, engine force forward, and air resistance backwards.

When drawing force vectors, remember that the length of each arrow should represent the size of the force. Use a consistent scale and label everything clearly.

Essential skill: Master free body diagrams early - they're the foundation for almost every mechanics problem you'll encounter!

Moments

A moment is the turning effect of a force around a pivot point. The formula is simple: Moment = force × perpendicular distance. The key word here is perpendicular - you need the shortest distance from the pivot to the line of action of the force.

For equilibrium problems, anticlockwise moments = clockwise moments. In the example shown, 400N × 1.5m = (300N × 1.0m) + (F × 1.5m), which gives F = 200N downwards.

A couple is a special case - two equal and parallel forces acting in opposite directions. They create pure rotation without any translational movement.

Memory trick: Think of a spanner - the longer the handle, the easier it is to turn a nut because you're increasing the perpendicular distance!

Centre of Mass and Moments

The centre of mass is where you can imagine all the weight of an object acting from a single point. For a uniform object, it's right in the geometric centre, but for irregular shapes, you'll need to calculate it.

When an object tips, it becomes unstable once its centre of mass moves outside its base of support. The bus example shows this perfectly - as long as the centre of mass stays over the wheels, it won't topple.

Understanding this concept helps explain why racing cars are built low and wide, while double-decker buses have specific weight limits for the upper deck.

Real-world connection: This is why you lean into corners when cycling - you're keeping your combined centre of mass over your bike's contact points!

Centre of Mass Calculations

Working out where the centre of mass lies involves balancing moments about a chosen point. Take each mass, multiply by its distance from your reference point, then find where everything balances.

In the example with people on a beam, you multiply each person's weight by their position: (100×9.81×0) + (90×9.81×0.5) + (80×9.81×0.2) on one side equals the balancing forces on the other side.

Solve for the unknown distance $x = 1.85m in this case$. This tells you exactly where to place your pivot point for equilibrium.

Exam tip: Always work in consistent units throughout - don't mix kilograms with Newtons or metres with centimetres!

Uniform Acceleration

These five kinematic equations are your toolkit for any motion problem involving constant acceleration. The trick is identifying which variables you know and which one you need to find.

Speed tells you how fast something moves, while velocity includes direction. Displacement is the straight-line distance from start to finish (different from total distance travelled). Acceleration is how quickly velocity changes.

The equations work for any constant acceleration situation - cars speeding up, balls falling, or objects sliding down slopes. Just remember that acceleration can be negative (deceleration).

Study hack: Create a quick reference table showing which equation to use based on what you're given - it'll save precious time in exams!

Displacement-Time Graphs

The gradient of a displacement-time graph gives you velocity. A steep slope means high velocity, a gentle slope means low velocity, and a flat line means the object isn't moving.

Straight lines represent constant velocity, while curved lines show acceleration. If the curve gets steeper, the object is speeding up. If it gets flatter, it's slowing down.

A negative gradient means the object is moving back towards its starting point - the displacement is decreasing.

Visual learner tip: Practice sketching these graphs for everyday situations like walking to school or riding in a car - it makes the abstract concepts much more concrete!

Reading Motion Graphs

When dealing with curved displacement-time graphs, the instantaneous velocity at any point is found by drawing a tangent to the curve and measuring its gradient. This is different from average velocity over a longer time period.

The steeper the curve becomes, the greater the acceleration. A curve that bends upwards shows increasing velocity (positive acceleration), while one that bends downwards shows decreasing velocity.

Remember: velocity = change in displacement ÷ change in time. This applies whether you're finding average velocity over a long period or instantaneous velocity at a specific moment.

Practical approach: When analysing graphs, always start by identifying what each axis represents and what the units are - this prevents most common mistakes!