Equation Sheet - Final Exam, Study notes of Dynamics

Download Equation Sheet - Final Exam and more Study notes Dynamics in PDF only on Docsity! ME 274: Basic Mechanics II Fall 2016 December 12, 2016 Final Exam: Equation Sheet ~vP = ẋî+ ẏĵ = vP êt = ṙêr + rθ̇êθ ~aP = ẍî+ ÿĵ = v̇P êt + v2P ρ ên = (r̈ − rθ̇2)êr + (rθ̈ + 2ṙθ̇)êθ ~vB = ~vA + ~ω × ~rB/A ~aB = ~aA + ~α× ~rB/A + ~ω × ( ~ω × ~rB/A ) ~vB = ~vA + (~vB/A)rel + ~ω × ~rB/A ~aB = ~aA + (~aB/A)rel + ~α× ~rB/A + 2~ω × (~vB/A)rel + ~ω × ( ~ω × ~rB/A ) ~F = m~aG ~MA = IA~α+ ~rG/A ×m~aA T1 + V1 + Unc1→2 = T2 + V2 T = 1 2 mv2A + 1 2 IAω 2 +m~vA • (~ω × ~rG/A) m~vG1 + ∫ t2 t1 ∑ ~Fdt = m~vG2 ~HO1 + ∫ t2 t1 ∑ ~MOdt = ~HO2 ~HA1 + ∫ t2 t1 ∑ ~MAdt = ~HA2 ~HO = ~rP/O ×m~vP or ~HA = IA~ω e = −vBn2 − vAn2 vBn1 − vAn1 IG,disk = 1 2 mr2 IG,bar = 1 12 mL2 Mẍ+ Cẋ+Kx = F (t) ωn = √ K M 2ζωn = C M xP (t) = A cosωt+B sinωt Final Exam: Equation Sheet Page 1 of 1