speed
Δd/Δt
velocity (v)
Δs/Δt (rω for a spinning object)
acceleration (a)
Δv/Δt
angular velocity (ω)
Δθ/Δt
angular acceleration (α)
Δω/Δt or τ/I
degrees-to-radians (rad)
xº/(180/ω) or xº/57.3
radians-to-degrees (deg, º)
xº x (180/ω) or xº x 57.3
projectile motion equations
(1) v = u+ at
(2) v2 = u2 + 2as
(3) s = ut + ½ at
force (F)
m x a
force of gravity (Fg)
Gm1m2/r2, where G = 6.67 × 10-11 N·m2·kg-2
force of drag (form) (Fd)
kAv2 or Fd = CdρAv2
Bernoulli’s equation
p + ½ ρv2 + ρgh = constant
torque (moment of force) (τ)
F × d, where d is the moment arm of force, or τ = Iα
sum of moments or sum of torques (ΣM or Στ)
τt = τ1 + τ2 + τ3 …
momentum (M)
m × v
angular momentum (H or L)
Iω or mk2ω
conservation of momentum
m1v1 = m2v2
angular impulse–momentum relationship
τ·t = Iω
impulse (J)
F × t or Δmv
inertia
m
moment of inertia (I)
Σmr2 or mk2
total moment of inertia (parallel axes theorem) (Itot)
ICM + md2
work (W)
F × d
power (P)
F × v or W/t
kinetic energy (KE)
½ mv2
potential energy (PE)
m × g × h
total energy (Etot)
KE + PE (assuming no change in thermal energy)
coefficient of restitution (e)
friction (Ff)
µR
coefficient of variation (CV)
SD/mean × 100%
sine rule
sin θ = opposite side/hypotenuse
cosine rule
cos θ = adjacent side/hypotenuse
tan rule
tan θ = opposite side/adjacent side
m·s-1 to km·h-1
x m·s-1 /1000 × 3600
km·h-1 to m·s-1
x km·h-1 × 1000/3600
time per frame (video)
1/frame rate
scaling factor
measured length/true length in real-world
units