Chapter 1 — Kinematics
Motion described by displacement, velocity, acceleration and time — without asking why
Links final velocity to initial velocity with constant acceleration over time. The simplest SUVAT equation.
Total distance covered by an accelerating object. The ½at² term captures how acceleration builds up distance over time.
Relates velocity and displacement without needing time — useful when time is unknown or irrelevant.
Displacement equals the average of initial and final velocity multiplied by time — only valid under uniform acceleration.
Horizontal distance a projectile travels before landing. Maximum range is at θ = 45°.
Maximum altitude reached when the vertical component of velocity becomes zero.
Chapter 2 — Newton's Laws of Motion
The three fundamental laws that describe how forces cause or prevent change in motion
Net force on an object equals its mass times acceleration. The central equation of classical mechanics.
Gravitational force on an object. Weight is a force, mass is not — a common confusion point.
Maximum friction force is proportional to the normal contact force. μ (mu) depends on the surfaces in contact.
Component of gravity perpendicular to an inclined surface — the surface pushes back with this force.
Force pulling an object down the slope minus friction opposing that motion.
Acceleration of two unequal masses over a frictionless pulley. Net force divided by total mass.
Chapter 3 — Work, Energy & Power
Energy is the capacity to do work; power is the rate at which work is done
Energy transferred when a force moves an object. Only the component of force in the direction of motion counts.
Energy an object has due to its motion. Doubling speed quadruples KE — why speed limits matter.
Energy stored by an object by virtue of its height above a reference point. Converts to KE as it falls.
Energy stored in a compressed or stretched spring. Depends on the spring constant and the square of extension.
The net work done on an object equals its change in kinetic energy. Unifies force and energy perspectives.
Rate of doing work. Also equals force × velocity when force and velocity are in the same direction.
Fraction of input energy that is converted to useful output. No machine is 100% efficient due to friction and heat losses.
The restoring force in a spring is proportional to its extension — valid within the elastic limit only.
Chapter 4 — Momentum & Impulse
Momentum is conserved in all collisions; impulse links force and change in momentum
Quantity of motion an object has. A vector — direction matters. Conserved when no external forces act.
Total momentum before a collision equals total momentum after, provided no external forces act on the system.
Impulse is the change in momentum. A large force over a short time (crash) or small force over long time produce the same Δp.
v₂ = 2m₁u₁ / (m₁+m₂)
In a perfectly elastic collision, both momentum AND kinetic energy are conserved.
Objects stick together after collision. Momentum conserved, but KE is lost to heat/deformation.
Ratio of relative speed after to before collision. e = 1: perfectly elastic; e = 0: perfectly inelastic.
Chapter 5 — Circular Motion
Objects moving in circles always accelerate toward the centre — centripetal acceleration
Rate of angular change — how many radians per second the object rotates. Links to period T and frequency f.
Tangential (linear) speed of a point on a rotating object. Increases with radius — why the outer edge of a disc moves faster.
Acceleration directed toward the centre, always perpendicular to velocity. Not slowing the object — changing its direction.
Net force needed to maintain circular motion. NOT a new force — provided by friction, tension, gravity, or normal force.
Angle a conical pendulum makes with vertical, balancing horizontal centripetal force and vertical weight component.
Minimum speed at the top of a loop where gravity alone provides centripetal force (normal force = 0).
Chapter 6 — Gravitation
Newton's universal law of gravitation governs planetary orbits, tides, and weight
Every mass attracts every other mass. Force falls off with the square of separation — an inverse-square law.
Field strength at distance r from a mass M — numerically equals the free-fall acceleration at that point.
Negative because gravity is attractive — energy is released as objects move closer. Zero at infinity.
Speed for a circular orbit at radius r. Gravity provides the exact centripetal force needed — no engine required.
Period of orbit squared is proportional to the cube of the orbital radius. Holds for all bodies orbiting the same central mass.
Minimum speed to escape a planet's gravity permanently — KE must overcome negative GPE.
Chapter 7 — Rotational Motion
Rotational analogues of Newton's laws — torque, angular momentum, and moment of inertia
Rotational equivalent of force. The turning effect of a force about a pivot. Maximised when force is perpendicular to the lever arm.
Rotational inertia — resistance to change in rotation. Depends on how mass is distributed relative to the axis.
Net torque equals moment of inertia times angular acceleration — exact rotational analogue of F = ma.
Conserved when no external torque acts. Explains why spinning objects resist changing their axis of rotation.
Energy stored in rotation. A rolling object has both translational and rotational KE simultaneously.
When rolling without slipping, the contact point is momentarily at rest. Linear velocity of centre = ωr.
Common Mistakes in Mechanics
Confusing mass and weight
Mass (kg) is the amount of matter. Weight (N) is the gravitational force on it. They are not the same thing, and differ on other planets.
Always: W = mg, not W = mMixing up distance and displacement
Distance is scalar (total path), displacement is vector (shortest path from start to end). Average speed ≠ average velocity.
Displacement considers directionApplying SUVAT to non-constant acceleration
SUVAT equations (v = u + at, etc.) are only valid when acceleration is uniform. Do NOT use them if acceleration varies with time.
Check: is a constant throughout?Forgetting the ½ in KE and EPE
KE = ½mv² and EPE = ½kx² both have the factor of ½. A very common slip that doubles or halves the answer.
Both have ½ — always checkNot drawing a free-body diagram
Jumping straight into equations without identifying all forces leads to missing gravity, normal force, or friction. FBD is non-negotiable.
Draw FBD for every mechanics problemMixing sine and cosine on inclines
Along an incline: F_parallel = mg·sinθ. Perpendicular (normal): N = mg·cosθ. Swapping these is one of the most common errors in A-level.
Parallel → sin; Perpendicular → cosTreating centripetal force as a separate force
Centripetal force is not a new type of force. It is provided by friction, tension, gravity, or the normal force — never add it separately in an FBD.
Ask: what force provides centripetal?Inconsistent sign conventions
Choosing upward as +ve in one step and then downward as +ve in another breaks everything. Set a direction at the start and stick to it.
Define +/− at the start, never changeAdding vector magnitudes directly
Velocity and force are vectors. You cannot add 3 m/s north + 4 m/s east = 7 m/s. You must resolve into components and use Pythagoras.
Always resolve vectors into componentsForgetting units and significant figures
Using km/h instead of m/s, or g instead of kg, corrupts every formula. Always convert to SI units before substituting.
Convert to SI first, alwaysConfusing velocity and speed at top of loop
At the top of a vertical loop, v_min = √(gr) gives SPEED. Students often forget to check direction and conserve energy to find bottom speed too.
Use energy conservation + Newton at topAssuming KE is conserved in all collisions
KE is only conserved in perfectly elastic collisions. In most real collisions (inelastic), KE is lost to heat, sound, or deformation.
Momentum always conserved; KE may not be