Fundamentals equations of dynamic, Cheat Sheet of Dynamics

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Fundamental Equations of Dynamics KINEMATICS Particle Rectilinear Motion Variable a Constant a dv - a= vemtad ds va 8 = Sy + ut + Za? ads =vdu vy = uf + 2a.(s — 5) Particle Curvilinear Motion x, y, 2 Coordinates 7, 6 z Coordinates ve=18 dp=r6 +276 wad n, t, b Coordinates [+ (ay/de, |d?y/ax?| Relative Motion Ye = Vat Vea fp = a4 + Apya Rigid Body Motion About a Fixed Axis Variable « Constant « = a, do @y + at = o= a, a ‘at 0 red 4@ w= 8 = Oy + wnt + fart? dt wda = add w = wh + 2a,(8 — A) For Point P s=6r v=er @=cr G,= o'r Relative General Plane Motion—Transtating Axes Va = Vat Vajacpiny Aa = 8a + AB/a(pin) Relative General Plane Motion—Trans. and Rot. Axis Ve = Vat OX ra + (Vaja)aye ag = ag t OX ry, + OX (OX Faye) + 20. X (vaya)eye + (Azja)aye KINETICS Mass Moment of Inertia / = / 7 din Parallel-Axis Theorem 1 = Ig + ma? T TT Equations of Motion Particle ZF = ma Rigid Body =F, = mag) (Plane Motion) ZF, = m(aa), SMg=lga or EMp=T( Mp Principle of Work and Energy Tt+hr2=-h Kinetic Energy Particle Rigid Body (Plane Motion) = wd, + } igo? Work Variable force Up = / F cos @ ds Constant force Ur = (F,cos8) As Weight Uy = — Way Spring U, = —(b ks} - 5 ks?) Couple moment Uy = M A@ Power and Efficiency a Pout _ Your p=—=F- = Aut _, Sout dt ve P, an Conservation of Energy Theorem Tht+Vy=Hh+th Potential Energy V=V,+¥, where V, = 4Wy,V, = ty ks? Principle of Linear Impulse and Momentum Particle my +t = / Fat 1 = s u mv) + x fr at Conservation of Linear Momentum L(syst. mv), = ¥ (syst. mv) Rigid Body m(va)o Coefficient of Restitution ¢ = (282 — @alz (va — (eh Principle of Angular Impulse and Momentum Particle (Ho) + 2 [Mo dt = (Ho)2 where Ho = (d)(mv) (He) + = [Mc dt = (Ae) where He = (Ho), + 3 [Mo dt = (He) Rigid Body (Plane motion) where Ho = Iow Conservation of Angular Momentum Gyrati Radius of Gyration Z(oyst. HD, = E (syst. Ha