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INTRODUCTION

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Force F = ma
Weight wt = mag
Pressure P = F/A
Density ρ = m/V
Torque T = Fd
Impulse J = Ft
Displacement d = Δ position
Velocity v = d/t
Acceleration

a = Δv/Δt

a = (v2 – v1)/(t2 – t1)

Equations of constant acceleration

v2 = v1 + at

d = v1t + ½ at2

v22 = v12 + 2ad

Angular displacement θ = Δ angular position
Angular velocity ω = θ/Δt
Angular acceleration

α = Δω/Δt

α = (ω2 – ω1)/(t2 – t1)

Curvilinear distance s = rΦ
Linear—angular velocity v = rω
Tangential acceleration

at = rα

at = (v2 – v1)/t

Radial acceleration ar = v2/r
Friction F = μR
Static friction Fm = μsR
Kinetic friction Fk = μkR
Linear momentum M = mv
Impulse—momentum Ft = ΔM
Coefficient of restitution –e = (v1 – v2)/(u1 – u2)
Work W = Fd
Power

P = W/Δt

P = Fv

Kinetic energy ½ mv2
Potential energy

PE = magh

PE = (weight)(height)

Strain energy SE = ½ kx2
Conservation of mechanical energy (PE + KE) = C
Principle of work and energy W = ΔKE + ΔPE + ΔTE
Equations of static equilibrium

ΣFv = 0

ΣFh = 0

ΣT = 0

Equations of dynamic equilibrium

ΣFx – max = 0

ΣFy − may = 0

ΣTG − Iα = 0

Segmental method for CG

Xcg = Σ(xs) (ms)/Σms

Ycg = Σ(ys) (ms)/Σms

Moment of inertia I = mk2
Moment of inertia (local term) Hl = Isωs
Moment of inertia (remote term) Hr = mr2ωg
Angular momentum

H = Iω

H = mk2ω

Segment angular momentum H = Isωs + mr2ωg
Angular impulse

Tt = ΔH

Tt = (Iω)2 – (Iω)1

Newton’s second law (angular) T = Iα
Centripetal force

Fc = mv2/r

Fc = mrω2

Buoyant force Fb = Vdγ
Drag FD = ½CDρApv2
Lift FL = ½CLρApv2

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