Newton's Laws of Motion

• Newton's first law: no resultant force means constant velocity (including rest).
• Newton's second law: resultant force = ma, with the acceleration in the direction of the resultant.
• Weight W = mg with g = 10 m s⁻².
• Connected particles: write F = ma for each particle; a light inextensible string has the same tension throughout and both ends share the same acceleration.
• On a rough slope the acceleration up the slope differs from the acceleration down it, because friction changes direction.

Resultant force in the direction of the acceleration

Draw the force diagram, decide the direction of the acceleration and write (sum of forces in that direction) = ma. Perpendicular to the motion, the forces balance (no acceleration there). Combine with suvat when you need distances or times — this is constant acceleration because the forces are constant.

Resistances other than friction (such as air resistance) are only included when the question mentions them. Vertical motion includes lifts: the reaction from the floor is the person's "apparent weight".

One equation per particle

For particles joined by a light inextensible string, the tension is the same at both ends and both particles have the same magnitude of acceleration. Over a smooth pulley the tension is unchanged. Write F = ma separately for each particle in its own direction of motion, then add or solve simultaneously.

For a car towing a trailer, the tow-bar or rope carries a tension T when accelerating; a rigid tow-bar can also push, giving a thrust when braking. Treating the whole system as one body gives the acceleration quickly (internal forces cancel); then use one part to find T.