5 Kinematic Variables
SUVAT: s u v a t — 5 kinematic variables
5 Kinematic Variables
The five kinematic variables for motion problems
Displacement (s), Initial velocity (u), Final velocity (v), Acceleration (a), Time (t). Know any three → solve for the other two using the SUVAT equations.
Newton's Second Law
F = ma
Newton's Second Law
Force equals mass times acceleration — the core of mechanics
Double the force → double the acceleration. Double the mass → half the acceleration. Units: Newtons = kg·m/s². The most-used equation in all of physics.
Law of Inertia
Newton's 1st: objects keep doing what they're doing unless a net force acts
Law of Inertia
An object in motion stays in motion — inertia explained
No net force = no change in motion. Friction is the real-world force that stops things. In space, an object thrown forward travels forever.
Action-Reaction Pairs
Newton's 3rd: every action has an equal and opposite reaction
Action-Reaction Pairs
Forces always come in pairs — rockets, swimming, and walking use this
Rocket pushes gas backward → gas pushes rocket forward. You push on a wall → wall pushes back on you equally. The pair acts on different objects.
Energy Formulas
KE = ½mv² PE = mgh
Energy Formulas
Kinetic and potential energy — two formulas every physics student needs cold
KE: kinetic energy. Doubling speed quadruples KE (squared). PE: gravitational potential energy — depends on height. Total mechanical energy = KE + PE (conserved without friction).
Work Formula
Work = Force × distance × cosθ. Energy is transferred only when force has a component along motion.
Work Formula
Work is done only when force causes displacement in the direction of the force
W = Fd cosθ. If force is perpendicular to motion (θ=90°), no work is done — cos90°=0. Carrying a heavy box horizontally: you do no work on the box (you push up, it moves sideways). Units: Joules = Newton·meters.
Conservation of Momentum
Conservation of momentum: m₁v₁ + m₂v₂ = m₁v₁' + m₂v₂' — total momentum unchanged in closed system
Conservation of Momentum
Total momentum before a collision equals total momentum after
Elastic collision: both momentum AND kinetic energy conserved (billiard balls). Inelastic collision: only momentum conserved, KE lost to heat/sound (car crash). Perfectly inelastic: objects stick together, maximum KE lost. Momentum is always conserved in a closed system.
Centripetal Force
Circular motion: centripetal force = mv²/r, always directed toward center
Centripetal Force
The inward force that keeps objects moving in a circle
Centripetal means 'center-seeking.' For circular motion, a net force must point toward the center. This is NOT a new force — it's provided by existing forces: tension in a string, gravity for orbiting satellites, friction for a car turning. Remove the centripetal force → object flies off in a straight line.
Newton's Law of Gravitation
Gravitational force: F = Gm₁m₂/r². Double distance → force drops to ¼.
Newton's Law of Gravitation
Gravity between any two masses — follows an inverse square law
G = 6.674×10⁻¹¹ N·m²/kg². Force depends on product of masses and inversely on distance squared. Double the distance → (1/2)² = ¼ the force. The same law that makes apples fall also keeps the Moon in orbit.
Simple Harmonic Motion
Simple harmonic motion: restoring force ∝ displacement. Period of pendulum: T = 2π√(L/g)
Simple Harmonic Motion
Oscillating systems where restoring force is proportional to displacement
Examples: pendulum, mass on spring. Restoring force always acts opposite to displacement. Period of simple pendulum T = 2π√(L/g) — depends only on length and gravity, NOT mass or amplitude (for small angles). Period of spring: T = 2π√(m/k) where k = spring constant.
Projectile Motion
Projectile motion: horizontal and vertical motion are INDEPENDENT. Horizontal: constant. Vertical: gravity.
Projectile Motion
Two independent motions happening simultaneously
Horizontal: constant velocity (no acceleration, ignoring air resistance). Vertical: constant acceleration due to gravity (9.8 m/s² downward). At peak: vertical velocity = 0, horizontal velocity unchanged. Range formula: R = v²sin(2θ)/g. Maximum range at 45°.
Torque
Torque = Force × lever arm. Clockwise = negative. Counterclockwise = positive.
Torque
The rotational equivalent of force
τ = r × F × sinθ. The longer the lever arm (r), the more torque for the same force. Opening a door: push near the hinges (short lever arm, little torque). Push at the handle (long lever arm, more torque). Torque causes angular acceleration just as force causes linear acceleration.