BZE formula sheet (full) - BZE Formula Sheet Rotational...

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BZE Formula Sheet Rotational Kinematics t v d dt r θ ω = = t a d dt r ω α = = 2 2 t r v a r r ω = = t t dv a r dt α = = Constant acceleration f i t ω ω α = + ( ) 2 1 2 f i i t t θ θ ω α = + ∆ + 2 2 2 f i ω ω α θ = + Rotational Dynamics net net dL M I dt τ α = = = G G G G M r F τ = = × G G G G L r mv I ω = × = G G G G 2 2 i i i I m r r dm = = 2 cm I I Ad = + For common shapes: 2 2 ,solid sphere 5 cm I mR = 2 1 ,disk or cylinder 2 cm I mR = 2 1 ,thin rod 12 cm I mL = Energy 2 1 point mass 2 K mv = 2 1 rot. object 2 K I ω = gravity U mgh = ( ) 2 1 spring 2 U k s = conservation: Mechanical tot tot E U K = + 2 1 pure rotation 2 cm E I mgy ω = + 2 2 1 1 rolling 2 2 cm cm E I mv mgy ω = + + W F ds = G G (Ideal) Fluids F p A = static o p p gh ρ = + gauge atm p p p = 2 1 2 Constant p v gh ρ ρ + + = 1 1 2 2 Av A v = Often used data: 3 fresh water 1000 kg m ρ = 3 air 1.28 kg m ρ = atm 101.325 p kPa = 1Pa=1N/m 2 1N/mm 2 =1MPa Direct Stress & Strain E σ ε = F A σ = and axial L L δ ε = latteral axial ε νε = − (1 2 ) V V δ ε ν = Special case: thin walled cylinders , 2 4 Hoop length pD pD t t σ σ = = Often used data: E steel =200GPa E Aluminum =70GPa E Bronze =100GPa E copper =120GPa Bending Stress , bending XX XX My I σ = special case: max max XX My M I Z σ = = Shear Stress Avg V A τ = G τ γ = x Q Ay I b τ
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  • Fall '09
  • MS.SIMPSON
  • Trigraph, special case, dL dt, Esteel=200GPa EAluminum=70GPa EBronze=100GPa, Pearson/Prentice Hall Publishing

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