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# EP-1 - Fundamental Equations of Dynamics KINEMATICS...

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Unformatted text preview: Fundamental Equations of Dynamics KINEMATICS Particle Reetilinear Motion Variable a Constant a = or a = g e = v" + act o=£ s=sﬂ+crﬂt+lat2 dt 2 C ads=ode e2=oﬁ+2a€(s—so) Particle Curvilinear Motion x, y, z Coordinates r; 9, z Coordinates a,=F —r62 1:1 = i: ax = if t), = r ey=y aJ,=3/ oa=rfi a3=ré+2ré ez=i az=E ez=z' az='z' n, i, b Coordinates o = s' ar = it = oﬂ ds 1:2 [1 + (dy/dxlzlm a” = F p = IdZy/dle Relative Motion VB = VA “ “std. as = “A + “BM Rigid Body Motion About a Fixed Axis Variable a Constant a = ac do: 05:? w=wo+act d9 1 2 «i=5 9=90+wot+§occt wdm=ad8 w3=mﬁ+2dc(e—eﬂ) ForPointP s=l9r v=wr a,=otr a,,=w2r Relative General Plane Motion—Translating Axes Vs = VA + vaAmin) as = 3A + anAwin) Relative General Plane Motion —Trans. and Rot. Axis v5 = VA + (1 X 78M + “3“)”: a3=aA+Q><r3M+QX(QXrBM}+ 20 X (VBJAnyz + (”some KINETICS Mass Moment of Inertia I = frz dm Parallel-Axis Theorem I = 1'0 + mdz Radius of Gyration k = % Equations of Motion Particle | SE = ma Rigid Body 2F); = more» (Plane Motion) 21"} = FRO-3(3)}: EMG=lGa 0r EMP=E{Mk)P Principle of Work and Energy T1 + 01.2 = T2 Kinetic Energy Particle ‘ T = grim: Rigid Body (Plane Motion) T = %mv§; + %le2 Work Variable force Up = j F cos 6 ds Constant force Up = (F; cos 6) As Weight Uw = - W Ay Spring illI = -(% 163% — ﬂat?) Couple moment UM = M A6 Power and Elliciency _ﬂ_ _ Pout_ Uout P — di — F v E — Pi — Ui Conservation of Energy Theorem T1 + Vl = T2 + Vz Potential Energy V = Vg + Va. where Vg = iWy. Va = +% its2 Principle of Linear Impulse and Momentum Particle ‘ mvl + E f F dt = mvz Rigid Body ‘ m(vG)1 + Z/F dt = nihrG)2 Conservation of Linear Momentum E{syst.mv)1 = E(syst.mv)2 Coefﬁcient of Restitution e = m (”Ah—(”sh Principle of Angular Impulse and Momentum Particle (Hoh + Z/Mo d3 = (Ho): where Ho = (d)(rnv) H + E/M df = H Rigid Body ( “)1 G ( G): where HG = le (Hoh + 2/340 d3 = (Ho): where H0 = low (Plane motion) Conservation of Angular Momentum E{syst.I-l)1 = 2(systJ-I); ...
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