Memory tricks for forces and motion

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.

No net force = no change in motion. Friction is the real-world force that stops things. In space, an object thrown forward travels forever.

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.

KE: kinetic energy. Doubling speed quadruples KE (squared). PE: gravitational potential energy — depends on height. Total mechanical energy = KE + PE (conserved without friction).

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.

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 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.

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.

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.

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°.

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.

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.

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.

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.

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.