Proven Mnemonics & Acronyms — fast to learn, hard to forget.
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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.
Rotational Kinematics
Every linear equation has a rotational twin — swap x→θ, v→ω, a→α, m→I
Linear to rotational analogy — same equations, different variables
Rotational motion follows identical math to linear motion — just with angular quantities
Linear → Rotational: displacement x → angle θ (radians). Velocity v → angular velocity ω (rad/s). Acceleration a → angular acceleration α (rad/s²). Mass m → moment of inertia I. Force F → torque τ. Newton's 2nd: F=ma → τ=Iα. Kinetic energy: ½mv² → ½Iω². Momentum: p=mv → L=Iω. Rolling without slipping: v_cm = ωr. Moment of inertia depends on mass distribution: solid cylinder = ½mr², hollow cylinder = mr², solid sphere = 2/5 mr².
τ = Iα
Rotational Newton's 2nd — torque = moment of inertia × angular acceleration
L = Iω
Angular momentum — conserved when net torque = 0
Rolling
v = ωr links linear and rotational — both KE terms add
Friction Forces
STATIC is stronger — object hasn't moved yet. KINETIC is weaker — once sliding.
Static vs kinetic friction — and how to calculate each
Static friction adjusts up to its maximum; kinetic friction is fixed once sliding begins
Static friction: f_s ≤ μ_s × N — adjusts to match applied force until maximum reached. Once object starts moving, switches to kinetic friction: f_k = μ_k × N (constant). Always: μ_s > μ_k (static coefficient larger than kinetic — harder to START sliding than to keep sliding). Normal force N = mg cos θ on an incline. Direction: friction always opposes relative motion (or tendency of motion). Kinetic friction does negative work on the sliding object — converts KE to heat.
Static
Adjustable 0 to μₛN — object not yet moving
Kinetic
Fixed = μₖN — once sliding, always this value
μₛ > μₖ
Always — harder to start moving than to keep moving
Impulse and Momentum
J = FΔt = Δp — impulse equals change in momentum
Impulse-momentum theorem — force × time changes momentum
A large force for a short time equals a small force for a long time — same impulse, same momentum change
Impulse J = F×Δt = Δp = m×Δv. Units: N·s = kg·m/s. Conservation of momentum: in a closed system, total momentum before = total momentum after. Elastic collision: both momentum AND kinetic energy conserved. Inelastic collision: only momentum conserved, KE lost. Perfectly inelastic: objects stick together — most KE lost. Real applications: airbags increase collision time Δt → reduce force F (same impulse = same momentum change). Crumple zones, catching a ball by pulling your hand back.
Elastic
Momentum AND kinetic energy both conserved
Inelastic
Only momentum conserved — KE converted to heat/deformation
Airbag logic
Larger Δt → smaller F — same impulse, safer stop
Fluid Mechanics Essentials
BPAC — Buoyancy, Pressure with depth, Archimedes, Continuity equation
Four core fluid mechanics concepts tested in introductory physics
Fluids follow pressure, buoyancy, and continuity — all connected by density
Pressure with depth: P = P₀ + ρgh — pressure increases linearly with depth. Archimedes' Principle: buoyant force = weight of fluid displaced = ρ_fluid × V_submerged × g. Object floats if ρ_object < ρ_fluid. Continuity equation: A₁v₁ = A₂v₂ — narrower pipe → faster flow (conservation of mass). Bernoulli's equation: P + ½ρv² + ρgh = constant — faster flow → lower pressure (explains lift, venturi effect). Pascal's Principle: pressure applied to enclosed fluid transmitted equally everywhere.
Buoyancy
F_b = ρ_fluid × V_sub × g — weight of displaced fluid
Continuity
A₁v₁ = A₂v₂ — narrow pipe, faster flow
Bernoulli
Faster flow → lower pressure — explains flight and carburetors
🎓 Common Exam Questions
Q: Explain the work-energy theorem and how it connects force, displacement, and kinetic energy.
A: The work-energy theorem states that the net work done on an object equals its change in kinetic energy: W_net = ΔKE = ½mv_f² − ½mv_i². Work done by a constant force: W = F·d·cosθ where θ is the angle between force and displacement. Only the component of force in the direction of motion does work. Conservative forces (gravity, spring) have associated potential energy — work done by them equals the decrease in potential energy. Non-conservative forces (friction, air resistance) convert mechanical energy to heat. Mechanical energy conservation: when only conservative forces act, KE + PE = constant. This is more powerful than Newton's laws for problems where the path is complex but the endpoints are known.
Q: Derive and explain the equations of projectile motion.
A: Projectile motion is analyzed by separating horizontal and vertical components — they are independent. Horizontal (no acceleration): x = v₀cosθ · t. Vertical (gravity only): y = v₀sinθ · t − ½gt². Velocity components: v_x = v₀cosθ (constant). v_y = v₀sinθ − gt. Time of flight: t = 2v₀sinθ/g. Range: R = v₀²sin(2θ)/g — maximum at θ = 45°. Maximum height: H = (v₀sinθ)²/2g. At any point, speed = √(v_x² + v_y²). At the top: v_y = 0, only v_x remains. The trajectory is a parabola. Air resistance complicates this — the optimal angle is less than 45° when drag is present.
Q: Explain rotational kinematics and the rotational analogs of Newton's laws.
A: Every linear quantity has a rotational analog: displacement x → angle θ (rad), velocity v → angular velocity ω (rad/s), acceleration a → angular acceleration α (rad/s²), mass m → moment of inertia I (kg·m²), force F → torque τ (N·m). Newton's 2nd for rotation: τ_net = Iα. Moment of inertia depends on mass distribution: I = Σmr² — farther mass from axis → larger I → harder to angularly accelerate. Common values: solid cylinder ½mr², hollow cylinder mr², solid sphere 2/5mr². Angular momentum: L = Iω. Conservation: if τ_net = 0, L is constant — ice skater pulling arms in reduces I, increases ω to keep L constant. Rolling without slipping: v_cm = ωr, total KE = ½mv² + ½Iω².
Q: What is the law of conservation of momentum and how does it apply to collisions?
A: Conservation of momentum: in a closed system with no external forces, total momentum p = Σmv is constant. Elastic collision: both momentum AND kinetic energy conserved. For two equal masses, velocities exchange. Inelastic collision: only momentum conserved, kinetic energy lost to heat, sound, deformation. Perfectly inelastic: objects stick together — maximum kinetic energy loss (consistent with momentum conservation). 1D elastic collision formulas: v₁' = (m₁−m₂)v₁/(m₁+m₂) and v₂' = 2m₁v₁/(m₁+m₂). 2D collisions: apply momentum conservation separately in x and y directions. Practical applications: rocket propulsion (gas expelled backward → rocket moves forward), car crash analysis, nuclear scattering experiments.
Q: Explain simple harmonic motion — conditions, equations, and energy.
A: Simple harmonic motion (SHM) occurs when a restoring force is proportional to displacement: F = −kx (Hooke's Law for springs). Differential equation: ẍ + (k/m)x = 0. Solution: x(t) = A cos(ωt + φ) where ω = √(k/m) for a spring, ω = √(g/L) for a simple pendulum (small angles). Period: T = 2π/ω. Frequency: f = ω/2π. Velocity: v = −Aω sin(ωt + φ). Acceleration: a = −Aω² cos(ωt + φ) = −ω²x. Energy: total E = ½kA² (constant). KE = ½mv² = ½k(A²−x²). PE = ½kx². Maximum velocity at x = 0: v_max = Aω. Maximum acceleration at x = ±A: a_max = Aω². Period of a spring-mass system is independent of amplitude — key property of SHM.