Scalars and vectors, resolving and combining forces, free-body diagrams, Newton's three laws of motion, weight, friction and the conditions for equilibrium and moments.

What this dot point is asking

Edexcel wants you to distinguish scalars from vectors, resolve and combine forces, draw free-body diagrams, state and apply Newton's three laws, work with weight and friction, and use the conditions for equilibrium including the principle of moments.

The answer

Scalars, vectors and resolving

To add vectors, either draw them tip-to-tail and measure the resultant, or resolve each into components, add the components separately, and recombine using Pythagoras and trigonometry. Resolving is the workhorse of mechanics: choose convenient axes (often along and perpendicular to an incline) so that one component lines up with the motion.

Newton's three laws

The second law is the key calculating tool: find the resultant force, then $a = \frac{F}{m}$. The third law explains rocket propulsion, walking, and why a book on a table is not the same Newton pair as the table pushing the book up (that is the normal contact pair with the book pushing down on the table).

Weight, friction and free-body diagrams

Weight is the gravitational force $W = mg$, acting from the centre of mass. Friction opposes relative sliding and depends on the surfaces and the normal contact force, not on the contact area. A free-body diagram shows one chosen body with every force acting on it (weight, normal contact force, tension, friction, applied force) drawn as arrows from the body; it is the essential first step before resolving and applying $F = ma$.

Equilibrium and moments

For a body in equilibrium under three forces, the three force vectors form a closed triangle. Choosing to take moments about the point where an unknown force acts eliminates that force from the equation, simplifying the algebra.

Examples in context

A climber's rope tension and the normal force from the rock are resolved to check equilibrium on a slope. A crane's jib is analysed with moments to keep the load balanced about the pivot. Seat belts and crumple zones apply Newton's second law in the momentum form to reduce the force during a crash. A rocket rises by Newton's third law, expelling exhaust gas backwards so the gas pushes the rocket forwards. A ladder against a wall is a classic three-force equilibrium-and-moments problem.

Try this

Q1. State Newton's second law in its momentum form. [1 mark]

• Cue. The resultant force equals the rate of change of momentum, $F = \frac{\Delta p}{\Delta t}$.

Q2. A force of $20$ N acts at $60$ degrees to the horizontal. Find its horizontal component. [2 marks]

• Cue. $F_x = 20\cos 60 = 10$ N.

Q3. A $0.50$ m spanner needs a moment of $15$ N m to loosen a bolt. Find the perpendicular force required at the end. [2 marks]

• Cue. $F = \frac{\text{moment}}{d} = \frac{15}{0.50} = 30$ N.