Apply Newton's three laws of motion to objects modelled as point masses.

What this dot point is asking

This dot point asks you to connect the forces on an object to its motion. The object is modelled as a point mass, so you can ignore its size and treat every force as acting at one point.

Newton's first law

An object continues at rest or at constant velocity unless a net external force acts on it. This is the law of inertia: motion does not need a force to keep it going, only a force to change it. A puck sliding on frictionless ice would never stop. In real life friction and air resistance are the net forces that bring things to rest.

Newton's second law

The net force on an object equals its mass times its acceleration:

Force is a vector, so this equation holds separately in each direction. The acceleration is always in the same direction as the net force. A larger mass needs a larger force to reach the same acceleration, which is why mass measures inertia.

Newton's third law

When object A exerts a force on object B, object B exerts an equal and opposite force on A. The two forces are the same size, opposite in direction, and always act on different objects, so they never cancel each other on the same body. A swimmer pushes water backward and the water pushes the swimmer forward.

Common forces and free body diagrams

To analyse a situation, draw a free body diagram showing only the forces on the one object you care about:

• Weight $W = mg$ acts downward from the centre of mass.
• The normal force $N$ acts perpendicular to a surface.
• Friction $f$ acts along a surface, opposing relative motion.
• Tension $T$ acts along a rope or string, pulling away from the object.

When forces act at angles, resolve each into components along convenient axes (often horizontal and vertical, or along and perpendicular to a slope), then apply $F_\text{net} = ma$ to each axis separately.

Friction and motion on a slope

Friction is modelled as $f = \mu N$, where $\mu$ is the coefficient of friction and $N$ is the normal force. On a slope of angle $\theta$, resolving the weight gives a component $mg\sin\theta$ down the slope and $mg\cos\theta$ into the surface (so $N = mg\cos\theta$ for an object on an incline with no other vertical forces). An object slides only when the driving component $mg\sin\theta$ exceeds the maximum friction $\mu mg\cos\theta$, which is why the angle at which sliding begins gives $\mu = \tan\theta$.

In the exam, always start with a labelled free body diagram, choose your axes, resolve angled forces, then write $F_\text{net} = ma$ for each direction. Treating an equilibrium problem as $F_\text{net} = 0$ and an accelerating problem as $F_\text{net} = ma$ keeps your method clear.