Mechanics — Complete Formula & Method Cheat Sheet
Newton's Laws, momentum, impulse, work-energy-power. Every formula, every definition, every method. All data sourced directly from the CAPS curriculum and the Everything Science Grade 12 textbook. 65 marks of Paper 1 in one document.
Newton's Three Laws — Exact CAPS Definitions
The exam asks "State Newton's [First/Second/Third] Law" for 2 marks each. These must be word-perfect.
Every object continues in its state of rest or uniform motion in a straight line, unless it is compelled to change that state by a net force acting on it.
The net force acting on an object is equal to the rate of change of momentum of that object in the direction of the net force.
F_net = Δp/Δt — the general form (Grade 12)
F_net = ma — when mass is constant
When object A exerts a force on object B, object B simultaneously exerts an equal but opposite force on object A.
These forces act on DIFFERENT objects. They are equal in magnitude, opposite in direction, and the same type of force. Students lose marks by saying they act on the same object.
Free Body Diagrams
Every mechanics calculation starts here. Skip it and you will miss a force.
| Force | Symbol | Direction | Include When |
|---|---|---|---|
| Weight | Fg / W | Straight down | Always |
| Normal force | N / FN | ⊥ to surface | Object on a surface |
| Friction | f / Ff | Opposite to motion | Surface is rough |
| Applied force | FA | As stated | Pushing / pulling |
| Tension | T / FT | Along the string | Connected by rope |
Inclined Plane Components
KEY TOPICOn an incline at angle θ, weight resolves into two components:
Component ∥ to slope = mg sinθ (down the incline)
Component ⊥ to slope = mg cosθ
Normal force N = mg cosθ (NOT mg)
Friction f = μN = μmg cosθ
Using mg instead of mg cosθ for the normal force on an incline. This gives the wrong friction and ruins the entire calculation. The examiner report flags this every single year.
Momentum and Impulse
The linear momentum of an object is a vector quantity equal to the product of the mass and velocity of the object.
p = mv Unit: kg.m.s⁻¹ Direction: same as velocity
The total linear momentum of an isolated system remains constant (is conserved) provided no external net force acts on the system.
m₁v₁ᵢ + m₂v₂ᵢ = m₁v₁f + m₂v₂f
| Collision Type | What Happens | Momentum? | Ek? |
|---|---|---|---|
| Elastic | Bounce, no energy lost | Conserved | Conserved |
| Inelastic | Bounce, some energy lost | Conserved | Not conserved |
| Perfectly inelastic | Stick together | Conserved | Not conserved |
Impulse is the product of the net force acting on an object and the time interval for which the force acts.
Impulse = F_net · Δt = Δp = mv_f - mv_i
For a given Δp, increasing Δt reduces F_net. Airbags, crumple zones, and bending your knees when landing all increase the time of impact, reducing the force on the body.
Work, Energy and Power
Work Done
W = FΔx cosθ
| Situation | θ | cosθ | Work |
|---|---|---|---|
| Force and motion same direction | 0° | 1 | Positive |
| Force and motion opposite | 180° | -1 | Negative |
| Force ⊥ to motion | 90° | 0 | Zero |
Energy Formulas
Ek = ½mv² — kinetic energy (energy of motion)
Ep = mgh — gravitational potential energy (energy of height)
The net work done on an object is equal to the change in its kinetic energy.
W_net = ΔEk = ½mv_f² - ½mv_i²
| Smooth surface (no friction) | Ek_i + Ep_i = Ek_f + Ep_f |
| Rough surface (friction present) | Ek_i + Ep_i + W_nc = Ek_f + Ep_f |
| Any situation (always works) | W_net = ΔEk |
Read the question for "smooth" or "rough." That tells you which equation.
Power
P = W/Δt — power is rate of doing work
P = Fv — when force and velocity are known
Unit: watts (W). 1 kW = 1000 W.
The Complete Mechanics Formula Sheet
How This Appears in the NSC Exam
| Topic | Questions | Marks | Full Guide |
|---|---|---|---|
| Newton's Laws | Q2-3 | 25-30 | Newton's Laws guide |
| Momentum / Impulse | Q3-4 | 15-20 | Momentum guide |
| Work / Energy / Power | Q4-5 | 20-25 | Work-Energy guide |
| Total Mechanics | ~65 |
The DBE loves combining topics. A question might use F_net = ma to find acceleration, kinematics for displacement, W = FΔx for work done, and P = W/Δt for power. All in one question. Be ready to chain formulas together.
Related Guides
| Topic | Link |
|---|---|
| Electricity & magnetism formulas | Electricity & Magnetism Cheat Sheet |
| Common exam errors | 10 Common Mistakes — Physical Science |
| Past paper strategy | How to Use Past Papers |
| Overall study plan | How to Study for Physical Science |
| Photoelectric effect theory | Photoelectric Effect Guide |
65 marks in one section. Get them right.
A-Game Academy teaches Grade 12 Physical Science live via Zoom. Mr Sawaya — 30 years NSC experience, SACE registered, CAPS specialist. Max 15 students per class.