BZE formula sheet (full)

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 α 2 2 t r v ar r t t dv dt Constant acceleration fi t ωω =+ () 2 1 2 fii tt θθ =+∆ + ∆ 22 2 Rotational Dynamics net net dL MI dt τα = G G G G M rF τ × G G G G L rm v I =× = G G G G ii i I mr r dm 2 cm I IA d 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 = gravity Um g h = 2 1 spring 2 Uk s =∆ conservation: Mechanical tot tot E UK 2 1 pure rotation 2 cm E Im g y 11 rolling E v m g y + WF d s =⋅ G G (Ideal) Fluids F p A = static o p pg h ρ gauge atm pp p =− 2 1 2 Constant pvg h ρρ ++ = 2 2 Av = Often used data: 3 fresh water 1000 kg m = 3 air 1.28 kg m = atm 101.325 p kPa = 1Pa=1N/m 2 1N/mm 2 =1MPa Direct Stress & Strain E σε = F A σ = and axial L L δ ε = latteral axial νε (1 2 ) V V ν Special case: thin walled cylinders , 24 Hoop length pD pD σσ Often used data: E steel =200GPa E Aluminum =70GPa E Bronze =100GPa E copper =120GPa Bending Stress , bending XX XX My I = special case: max max XX My M I Z Shear Stress Avg V A = G τγ = x QA y I b  =   where 2 x I by dy = See other side for I xx of typical areas
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This note was uploaded on 10/03/2010 for the course PHYS. 203-NYA-05 taught by Professor Ms.simpson during the Fall '09 term at Dawson College.

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

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