Newton's first and second laws: forces and acceleration

First law (the law of inertia): A particle stays at rest, or keeps moving with constant velocity in a straight line, unless a resultant force acts on it.

"No resultant force" means the forces are balanced: they cancel out. That is exactly what we did in the forces-equilibrium topic: balanced forces → zero acceleration.

Second law: The rate of change of momentum (momentum = mass × velocity) is proportional to the resultant force and takes place in the direction of that force. For a particle of constant mass, this simplifies to the famous equation:

$F = ma$

where $F$ is the resultant force (the vector sum of all forces), $m$ is the mass in kg, and $a$ is the acceleration in m s⁻².

The unit of force, the newton (N), is defined so that $1\ \text{N} = 1\ \text{kg m s}^{-2}$.

The syllabus mentions these specifically:

• Weight $W = mg$: acts vertically downwards. Use $g = 10\ \text{m s}^{-2}$.
• Normal reaction $R$: perpendicular to the contact surface.
• Friction $F$: along the surface, opposes sliding (or tendency to slide). When the particle is sliding (or just about to slide), $F = \mu R$, where $\mu$ (the Greek letter "mu") is the coefficient of friction, a number that measures how rough the surface is. Otherwise $F \le \mu R$. (Careful: in $F = ma$, $F$ means the resultant force, not friction.)
• Tension $T$: in a taut string or rope, pulls along its length.
• Thrust (or compression): in a rigid rod, pushes along its length. A string cannot push, a rod can push or pull.

In every problem, draw the force diagram first, then apply $F = ma$ in the direction of motion (or the direction you're analysing).