MTLE Physics (Grades 9-12) cheat sheet

Kinematics: v = v₀ + at, Δx = v₀t + ½at², v² = v₀² + 2aΔx apply only for constant acceleration; free fall uses a = g ≈ 9.8 m/s² downward with air resistance neglected.

Newton's laws: ΣF = ma defines net force; action–reaction pairs act on different bodies and never cancel on the same object; static friction satisfies f ≤ μsN, kinetic friction f = μkN.

Momentum and impulse: p = mv; impulse J = FΔt = Δp; total momentum is conserved in any collision, kinetic energy only in elastic collisions; perfectly inelastic collisions share a final velocity.

Circular motion and gravitation: centripetal acceleration a = v²/r directed toward the center; F = Gm₁m₂/r²; orbital speed v = √(GM/r); Kepler's third law T² ∝ r³.

Work, energy, power: W = Fd cosθ; KE = ½mv²; gravitational PE = mgh near Earth; spring PE = ½kx²; W_nc = ΔE; P = W/t = Fv.

Rotational mechanics: τ = rF sinθ; I = Σmr²; rotational KE = ½Iω²; angular momentum L = Iω conserved when net torque is zero; rolling without slipping links v = ωr.

Oscillations and waves: T = 2π√(m/k) for a mass–spring system and T = 2π√(L/g) for a pendulum; wave speed v = fλ; sound speed rises with temperature in air; standing waves fix nodes at boundaries.

Electricity and magnetism: Coulomb's law F = kq₁q₂/r²; Ohm's law V = IR; P = IV = I²R; resistors in series add, in parallel add as reciprocals; magnetic force F = qvB sinθ and F = BIL sinθ.

Fluids and thermodynamics: pressure P = F/A and P = P₀ + ρgh; buoyant force equals weight of displaced fluid; ideal gas PV = nRT; first law ΔU = Q − W with W done by the gas.

Kinematics: v = v₀ + at, Δx = v₀t + ½at², v² = v₀² + 2aΔx apply only for constant acceleration; free fall uses a = g ≈ 9.8 m/s² downward with air resistance neglected.

Newton's laws: ΣF = ma defines net force; action–reaction pairs act on different bodies and never cancel on the same object; static friction satisfies f ≤ μsN, kinetic friction f = μkN.

Momentum and impulse: p = mv; impulse J = FΔt = Δp; total momentum is conserved in any collision, kinetic energy only in elastic collisions; perfectly inelastic collisions share a final velocity.

Circular motion and gravitation: centripetal acceleration a = v²/r directed toward the center; F = Gm₁m₂/r²; orbital speed v = √(GM/r); Kepler's third law T² ∝ r³.

Work, energy, power: W = Fd cosθ; KE = ½mv²; gravitational PE = mgh near Earth; spring PE = ½kx²; W_nc = ΔE; P = W/t = Fv.

Rotational mechanics: τ = rF sinθ; I = Σmr²; rotational KE = ½Iω²; angular momentum L = Iω conserved when net torque is zero; rolling without slipping links v = ωr.

Oscillations and waves: T = 2π√(m/k) for a mass–spring system and T = 2π√(L/g) for a pendulum; wave speed v = fλ; sound speed rises with temperature in air; standing waves fix nodes at boundaries.

Electricity and magnetism: Coulomb's law F = kq₁q₂/r²; Ohm's law V = IR; P = IV = I²R; resistors in series add, in parallel add as reciprocals; magnetic force F = qvB sinθ and F = BIL sinθ.

Fluids and thermodynamics: pressure P = F/A and P = P₀ + ρgh; buoyant force equals weight of displaced fluid; ideal gas PV = nRT; first law ΔU = Q − W with W done by the gas.