Newton’s Laws of Motion

An object continues at rest or at constant velocity unless acted on by a resultant force. The everyday intuition that motion needs a continuous push is wrong — what needs a force is a $\text{change}$ in motion.

The examinable consequence is a conversion: whenever a question says an object is stationary, moving at constant speed, or at terminal velocity, it is telling you the resultant force is zero. That immediately gives you equations, because the forces in each direction must balance.

The reluctance of an object to change its motion is its $\text{inertia}$, and mass is the measure of it.

A resultant force produces an acceleration in the same direction, with $F=ma$ where $F$ is the $\text{resultant}$ — never a single force unless it is the only one.

The reliable method is a free-body diagram: draw the object alone, then every force acting $\text{on}$ it as an arrow from it, labelled. Nothing the object exerts on anything else belongs on the diagram.

Then choose a direction as positive, add the forces along it with signs, and apply $F=ma$. For two-dimensional problems, do this separately along each of two perpendicular axes.

For every force there is an equal and opposite force. Precisely: if A exerts a force on B, then B exerts an equal and opposite force on A. The pair are the same type of force, act along the same line, and — critically — act on $\text{different objects}$.

That last condition is what makes the classic exam trap. A book on a table has its weight (Earth pulls book) and the normal contact force (table pushes book). These are equal and opposite, but they are $\text{not}$ a third-law pair, because both act on the book and they are different types of force. They balance because of the first law, not the third.

The genuine partners are: the book pulls the Earth up with an equal gravitational force, and the book pushes down on the table with an equal contact force.

For objects joined by a rope or in contact, there are two useful moves. Treat the system as $\text{one object}$ to find the acceleration, since internal forces cancel in pairs and only external forces matter. Then look at one object $\text{alone}$ to find the internal force such as the tension.

An inextensible connection means both objects share the same acceleration, which is what makes the system approach valid in the first place.