Force as a vector, the resultant of forces, Newton's three laws of motion, weight and the relationship between mass and weight, connected particles, and resolving forces in two dimensions.

What this dot point is asking

AQA wants you to treat force as a vector, find resultant forces, apply Newton's three laws, relate mass and weight, solve problems involving connected particles, and resolve forces into components in two dimensions. This is the heart of mechanics: almost every problem reduces to drawing a force diagram and applying $F = ma$ in chosen directions.

Force as a vector and the resultant

Forces add as vectors. If several forces act on a body, the resultant is their vector sum, found by adding components in two perpendicular directions. A body is in equilibrium precisely when the resultant force is zero, which means the components in each direction separately sum to zero. Drawing a clear force diagram, with weight, normal reaction, tension, friction and any applied force, is the essential first step and is often worth marks in its own right.

Newton's laws

Newton's first law is the special case of the second with zero resultant force, giving equilibrium (rest or constant velocity). Newton's third law says that if body A exerts a force on body B, then B exerts an equal and opposite force on A. The key point for exams is that these two forces act on different bodies, so they never cancel when you analyse a single body.

Resolving forces in two dimensions

In two dimensions you resolve each force into perpendicular components, usually horizontal and vertical, or along and perpendicular to a slope, then apply $F = ma$ in each direction independently. A force $F$ at angle $\theta$ to a chosen axis has component $F\cos\theta$ along that axis and $F\sin\theta$ perpendicular to it. On an inclined plane it is almost always easier to resolve along and perpendicular to the slope than horizontally and vertically.

Connected particles

The light string assumption means its mass is negligible (so tension is uniform), and inextensible means the connected particles share one acceleration. For a system on a table with a hanging mass, the hanging mass drives the motion; for two hanging masses, the heavier one descends.