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 |