An object remains at rest or moves with constant velocity unless acted upon by a net external force. This is the law of inertia. 'Constant velocity' includes staying at rest (v = 0). Implication: if an object is not accelerating, the net force is zero — forces are balanced.
The net force on an object equals its mass times its acceleration: F_net = ma. This is a vector equation — direction of acceleration matches direction of net force. Steps: (1) Draw free-body diagram (FBD). (2) Resolve all forces. (3) Find F_net. (4) Apply F_net = ma to find the unknown.
For every action force, there is an equal and opposite reaction force. Critical detail: the two forces act on DIFFERENT objects. Example: you push a wall (action) — the wall pushes you back (reaction). These forces are equal in magnitude, opposite in direction, same type of force, but on different objects, so they do NOT cancel.
A FBD shows ALL forces acting on a single object as arrows from the object's centre. Standard forces: Weight (W = mg, downward), Normal force (N, perpendicular to surface), Friction (f, opposing motion), Tension (T, along string/rope), Applied force. Each force must be labelled with magnitude and direction. Resolve along axes, then apply F_net = ma.
Mass (kg) is the amount of matter in an object — a scalar, constant everywhere. Weight W = mg is a gravitational force (N) — a vector pointing downward. On the Moon, your mass is the same but your weight is less (g_Moon ≈ 1.6 m/s²). Never write 'weight = 70 kg' — weight is in Newtons.
Static friction: acts when surfaces are stationary relative to each other. Maximum static friction = μ_s · N. Kinetic (sliding) friction: acts when surfaces slide. f_k = μ_k · N. Always μ_k < μ_s — it is harder to start an object moving than to keep it moving. Friction always opposes the relative motion (or tendency of motion).
For an object on a slope of angle θ, resolve the weight W = mg into two components: along the slope: W sinθ (causes sliding), perpendicular to slope: W cosθ (determines N). The normal force N = mg cosθ (if no other perpendicular forces). Friction force = μ_k · mg cosθ. Net force along slope = mg sinθ − f.
The normal force is always perpendicular to the contact surface — it is a contact force from the surface pushing back. It adjusts to maintain equilibrium in the perpendicular direction. On a flat surface: N = mg. On a slope: N = mg cosθ. In a lift accelerating upward: N = m(g + a). In free fall: N = 0 (weightlessness).
When an object falls through a fluid, drag force increases with speed. Phase 1: F_drag < mg → net downward force → object accelerates. Phase 2: as speed increases, F_drag increases → acceleration decreases. Phase 3: F_drag = mg → F_net = 0 → constant maximum speed = terminal velocity. The v–t graph curves and flattens exponentially. Factors increasing terminal velocity: greater mass (more weight to overcome), smaller cross-section (less drag). Example: a skydiver face-down reaches ~55 m/s; head-down reaches ~90 m/s. A parachute dramatically increases drag area, reducing terminal velocity to ~5 m/s.
For objects connected by strings, treat the SYSTEM first to find acceleration, then isolate an object to find tension. Atwood machine (two masses over pulley): a = (m₁ − m₂)g/(m₁ + m₂); T = 2m₁m₂g/(m₁ + m₂). Two blocks on a surface connected by a string, force F on one: a = F/(m₁ + m₂); T = m₂ × a. Elevator problems: person of mass m in elevator accelerating at a: N = m(g + a) upward acceleration, N = m(g − a) downward acceleration. N = 0 in free fall (weightlessness).
A spring force is proportional to extension: F = kx (restoring form: F = −kx). k = spring constant (N/m), x = extension from natural length. Stiffer springs have larger k. Hooke's Law holds only in the elastic region (below elastic limit). Beyond the elastic limit, the spring deforms permanently. Combining springs: in series — 1/k_total = 1/k₁ + 1/k₂ (k_total < either k); in parallel — k_total = k₁ + k₂ (k_total > either k). Hooke's Law leads directly to SHM (see oscillations).
F–a Graph (Force vs. Acceleration)
slope: Slope = mass (kg)For a constant mass, F vs. a is a straight line through the origin. The gradient equals the mass of the object. Used to experimentally determine mass.
F–t Graph (Force vs. Time)
area: Area = impulse = Δp (kg·m/s)Area under this graph = impulse = change in momentum. Used in momentum and impulse calculations. A large force over a short time can have the same impulse as a small force over a long time.
Newton's 2nd law in its full form is F = Δp/Δt. Multiplying both sides by Δt gives FΔt = Δp — the impulse-momentum theorem.
💡Exam tip: Use momentum conservation when time is unknown. Use F = ma when forces and time are both given.
Centripetal force is NOT a new type of force — it is whatever real force points inward in your FBD (gravity, tension, friction, normal force). Always identify the real force first.
💡Exam tip: Set up your FBD, find which force points toward the centre, and set it equal to mv²/r.
Click any formula to see symbol definitions.
All formulas for this topic are in BINAS BINAS 35A4. In the exam you don't need to memorise the equations — but you must know which table to open and what every symbol means.