APPENDIX D

EQUATIONS

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)

eqn

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