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What stops a bridge from collapsing, or keeps a spinning shaft from flying apart? Advanced dynamics and statics takes the fundamentals further, into rotation, torque and the forces acting on real structures. You'll work with moments, moment of inertia and equilibrium: the tools engineers use to analyse whether something will...
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Now that you are familiar with how an object's velocity changes over time in linear motion, we now shift our focus to angular motion, where similar principles apply to rotational systems. Use this resource to gain insight into the rotational behaviour of objects, and better understand the dynamics of systems...
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- Physics
- Advanced dynamics and statics
Blocks and pulleys are used throughout engineering: in cranes, elevators, cable-driven machines and stage rigging. Use this resource to learn about pulley systems and how to analyse two-pulley systems. Pulley systems A pulley system uses a rope that passes around one or more pulleys to lift or move a load....
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- Physics
- Advanced dynamics and statics
Whenever a force is distributed across a surface, it acts through a single point called the centroid. Finding the centroid tells us where to apply the equivalent resultant force, which we need to analyse structural behaviour. Use this resource to learn how to locate the centroid for simple and composite...
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Even at constant speed, circular motion involves constant acceleration. Your velocity is always changing direction, even if its magnitude stays the same. This is what you feel when a car rounds a sharp bend or a rollercoaster carves through a loop. This resource introduces centripetal acceleration and the centripetal force...
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Sometimes an object speeds up or slows down at a steady rate. For example, a car joining a freeway may increase its speed by the same amount every second, or a dropped object (ignoring air resistance) gains about \(\mathbf{9.8}\,\textbf{m/s}\) of speed each second as it falls. In these situations, the...
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Core dynamics explores the forces that shape motion in the world around us – from the pull of gravity on a hillside to the physics behind a spinning wheel. You'll work with ideas like Newton's laws, friction, momentum and energy, building the skills to tackle the kinds of problems that...
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- Maths and statistics
- Vectors and matrices
- Vectors
Imagine navigating a hilly landscape, searching for the steepest ascent or smoothest descent—this is the essence of directional derivatives. These mathematical tools are vital in meteorology for predicting temperature changes along wind paths, in finance for analysing portfolio shifts, and in machine learning for optimising algorithms. Use this resource to...
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- Maths and statistics
- Vectors and matrices
- Vectors
The distance between a point in 3D space and a plane can be determined using vectors and trigonometry. This is handy in many situations, like making sure components are specific distances from certain planes in construction, determining distances between a airplane and a mountain or building in safe flight planning,...
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You already interact with electricity constantly but what's actually happening inside a circuit? These resources build the foundation for understanding and measuring it, introducing the key quantities: charge, current, voltage and power....
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- Maths and statistics
- Vectors and matrices
- Vectors
Uniquely defining a line for a vector in three-dimensional space is useful in a range of scenarios. In mechanical and civil engineering, they are needed to create models and analyse alignment. In computer graphics, they can be used to define paths for animations. In physics, they represent trajectories of particles...
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- Maths and statistics
- Vectors and matrices
- Vectors
Just as we can define an equation for a line in three dimensions, we can do the same for an entire plane–that is, we can define an equation that represents a two-dimensional space within a 3D space. A plane is a subset of three dimensional space. You can think of...
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- Physics
- Advanced dynamics and statics
When a crane lifts a load, a broadcasting tower is guyed by cables, or a lighting rig is suspended above a stage, the support forces act in three dimensions – not just up, down, left or right. Analysing these forces requires vector methods, which let us resolve, combine and project...
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Place a book on a tilted surface and it either slides down or stays put depending on the angle and how rough the surface is. What determines this? This resource helps you to understand the components of gravitational forces that affect this and use them to analyse forces on inclined...
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- Maths and statistics
- Vectors and matrices
- Vectors
Vectors can be used to determine whether two lines in 3D cross each other (or intersect), and identify the point at which they intersect. This is used in a variety of STEM disciplines, including detection of collisions between objects in robotics and modelling complex structures in computer graphics and game...
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- Maths and statistics
- Vectors and matrices
- Vectors
Two planes in 3D can intersect. Finding this intersection has many real-life applications, including the design of buildings in architecture, 3D rendering and modelling in computer graphics, and determining paths of movement in robotics. Use this resource to learn how to determine the angle between two intersecting planes and the...
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- Maths and statistics
- Vectors and matrices
- Vectors
Vectors are used to represent forces in physics, handle 2D and 3D manipulation with computer graphics, and to calculate the forces acting on materials in textiles. You also deal with vector quantities in your everyday life, from driving your car down the road to planning the shortest route to get...
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Before you can explain why something moves, you need to describe how it moves. Kinematics gives you the tools to do that. Use these resources to learn about the language and tools of motion, from linear and angular motion to constant and non‑constant acceleration....
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Linear motion is how an object moves in a straight line. To describe these motions, we need to know some technical terms like displacement, distance, velocity, speed and acceleration, and how to represent how they change over time. Use this resource to learn about the terms and their relationships to...
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Every time you charge your phone, flick a light switch or plug in a kettle, you are interacting with an electrical circuit. But what is actually happening inside it? Use this resource to learn about the key quantities used to describe and measure electricity, the calculations that connect them, and...
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- Physics
- Advanced dynamics and statics
Every time you open a door, tighten a bolt with a spanner, or adjust a bike's handlebars, you're creating a turning effect. The further from the pivot you apply a force, and the more directly you push, the stronger that effect. This turning effect is called a moment or torque,...
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- Physics
- Advanced dynamics and statics
The resistance of an object to rotation depends not just on how heavy it is, but on how its mass is distributed. This property is called moment of inertia. Use this resource to understand two forms of moment of inertia: mass moment of inertia (used in dynamics) and area moment...
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In everyday life you might notice that it is harder to stop a heavy truck than a light car at the same speed, or a fast tennis ball than a slow one. This is because of momentum – a measure of how hard it is to stop a moving object....
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In everyday life, forces are all around us, from the push of your feet on the ground when you start walking, to the pull of gravity that keeps you on Earth. Newton’s three laws of motion describe how these forces affect the way objects start moving, keep moving, or come...
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In many cases, acceleration changes over time. You see this when a car that has been stopped at a traffic light speeds up to \(\mathbf{60}\,\textbf{km/h}\) after the light changes to green. Acceleration also varies throughout a rollercoaster ride. Both of these scenarios demonstrate non-constant (or non-uniform) acceleration. Use this resource...
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Why does a cheap phone charger cable get warm and charge your phone slowly, or a longer extension cord sometimes struggle to power a kettle or hairdryer? The answer lies in the relationship between voltage, current and resistance. This resource introduces Ohm's law—one of the most used relationships in electronics—and...
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Unlike the fairy lights from the previous page, the appliances in your home are wired in parallel. This is why your refrigerator keeps running when your toaster fails. Each component sits on its own independent path, so a break in one branch doesn't affect the others. This resource builds on...
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- Maths and statistics
- Vectors and matrices
- Vectors
You will have learned that vectors can be resolved in two dimensions along the horizontal and vertical axes. It is also possible to resolve one vector along the line of another vector, instead of along the \(x\)- and \(y\)-axes. Often, in physics, engineering and mathematics courses, you are asked to...
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- Maths and statistics
- Vectors and matrices
- Vectors
Breaking vectors down into their components—or resolving them—makes it easier to add or subtract them, especially when dealing with vectors that don't act along the same line. You will encounter this in many areas of STEM, like when analysing forces involved in robotics, studying the projectile motion of objects launched...
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- Maths and statistics
- Vectors and matrices
- Vectors
There are two ways to multiply two vectors. Here, we will learn about the scalar product. It has many applications in STEM. For example, scalar products are used to calculate the work done by a system, in computer graphics to calculate the amount of light hitting surfaces, and in engineering...
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A single blown globe can knock out an entire string of fairy lights—because in a series circuit, all components share one continuous path, and a break anywhere stops current flowing everywhere. This resource builds on current, voltage and resistance to explore how series circuits behave, including how voltage is shared...
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- Physics
- Advanced dynamics and statics
When a bridge holds steady under traffic, or a bookshelf stays put under a heavy load, the structure is in static equilibrium. This means every force and every turning effect is perfectly balanced — nothing accelerates, nothing rotates. Use this resource to explore the two conditions for static equilibrium and...
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Without static friction, nothing would stay put. It is the force that keeps objects at rest when a force is applied – stopping a parked car from rolling down a hill, keeping your feet from sliding when you walk, and holding a stack of books in place on a tilted...
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- Maths and statistics
- Vectors and matrices
- Vectors
The vector product is another way to multiply two vectors. Just like scalar products, vector products have many broad applications, such as in electrical engineering, quantum physics, software development, game programming and statistics. Use this resource to learn more. The vector product is a vector resulting from multiplying the magnitudes...
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Push a box across the floor and you've done work. Drop a ball and it trades height for speed. Run a motor and you measure how fast it delivers energy. Work, energy and power are three ways of describing the same underlying physics. This resource shows you how they connect,...
