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Mechanics Formula Sheet
All classical mechanics equations: kinematics, dynamics, energy, momentum, gravitation, and circular motion.
Kinematics (SUVAT) Equations
Valid for constant acceleration only. Variables: s=displacement (m), u=initial velocity (m/s), v=final velocity (m/s), a=acceleration (m/s²), t=time (s).
Eq. 1 (no s)
v = u + at
Relates velocity and time; derived from definition of acceleration
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Free Fall
h = ½gt² | v = gt
g=9.8 m/s², downward. Set u=0 for drop from rest.
Projectile Range
R = v₀²sin(2θ)/g
Maximum at θ=45°; same range for complementary angles
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Newton's Laws and Dynamics
Weight
W = mg
g=9.8 m/s²; weight in Newtons differs from mass in kg
Friction (kinetic)
f_k = μ_k N
μ_k=kinetic friction coefficient, N=normal force (N)
Friction (static max)
f_s ≤ μ_s N
f_s max = μ_s N; static friction resists motion up to this
Universal Gravitation
F = Gm₁m₂/r²
G=6.674×10⁻¹¹ N·m²/kg²; r=center-to-center distance
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Escape Velocity
v_esc = √(2GM/R)
Minimum speed to escape gravity; v_esc(Earth)≈11.2 km/s
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Energy and Work
Gravitational PE
PE_g = mgh
h=height above reference; defined relative to chosen level
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Spring PE
PE_s = ½kx²
k=spring constant (N/m), x=displacement from equilibrium
Work-Energy Theorem
W_net = ΔKE
Net work = change in kinetic energy (fundamental result)
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Conservation (no friction)
KE₁+PE₁ = KE₂+PE₂
Total mechanical energy is constant without non-conservative forces
Momentum and Collisions
Impulse
J = FΔt = Δp
J=impulse (N·s); equals change in momentum
Coeff. of Restitution
e = |v_rel after|/|v_rel before|
e=1 elastic; e=0 perfectly inelastic