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Fundamental Equations of Dynamics KINEMATICS Particle Rectilinear Motion Variable a Constant a = ac dv v = v0 + act a= dt ds s = s0 + v0t + 12 act 2 v = dt a ds = v dv v 2 = v20 + 2ac(s - s0)

Equations of Motion Particle F = m a Rigid Body Fx = m(aG)x (Plane Motion) Fy = m(aG)y MG = IGa or MP = (mk)P Principle of Work and Energy T 1 + U1 - 2 = T 2 Kinetic Energy Particle T = 21mv2 Rigid Body (PlaneMotion) T = 21mvG2 + 1IG v2

Particle Curvilinear Motion x, y, z Coordinates r, u, z Coordinates 2 # # ## # ## ax = x vx = x Work vr = r ar = r - r u 2 # ## # ## # # UF = F cos u ds vy = y ay = y vu = r u au = r u + 2r u Variable force L # ## # ## az = z vz = z az = z Constant force UF = (Fc cos u)  s vz = z Weight UW = - W y n, t, b Coordinates Spring Us = - 1 12 ks 22 - 12 ks 21 2 # # dv Couple moment UM = Mu at = v = v v = s ds Power and Efficiency [1 + (dy >dx )2]3>2 v2 Uout Pout dU r = an = P = = e = = F#v r 0 d2y >dx 2 0 Uin Pin dt Relative Motion Conservation of Energy Theorem vB = vA + vB/A aB = aA + aB/A T1 + V 1 = T2 + V 2 Potential Energy Rigid Body Motion About a Fixed Axis V = V g + V e, where V g = {W y, V e = +21 ks 2 Variable a Constant a = ac Principle of Linear Impulse and Momentum dv a = v = v0 + act dt Particle mv 1 +  F dt = mv 2 du L v = u = u0 + v0t + 12act 2 dt Rigid Body m(v G)1 +  F dt = m(v G)2 v dv = a du v2 = v20 + 2ac(u - u0) L For Point P Conservation of Linear Momentum  (syst. mv)1 =  (syst. mv)2 s = ur v = vr at = ar an = v 2r (vB)2 - (vA)2 Coefficient of Restitution e = Relative General Plane Motion—Translating Axes (vA)1 - (vB)1 v B = v A + v B>A(pin) aB = aA + aB>A(pin) Principle of Angular Impulse and Momentum Relative General Plane Motion—Trans. and Rot. Axis Particle (HO)1 +  MO dt = (HO)2 v B = v A +  * rB>A + (v B>A )xyz L # where HO = (d)(mv) aB = aA +  * rB>A +  * (  * rB>A ) + (HG)1 +  MG dt = (HG)2 2 * (v B>A )xyz + (aB>A )xyz L KINETICS Rigid Body where HG = IGv (Plane motion) Mass Moment of Inertia I = r2 dm (HO)1 +  MO dt = (HO)2 L L 2 Parallel-Axis Theorem I = IG + md where HO = IOv Conservation of Angular Momentum I Radius of Gyration k = (syst. H)1 = (syst. H)2 Am...