University:
Eastern Kentucky University
Course:
PHY 131 | College Physics I
Academic year:

2022
Views:

70

Pages:

1
Author:

esfredint7qo

Fundamental Equations of Dynamics KINEMATICS Particle Rectilinear Motion Variable a Constant a = ac dv a= v = v0 + a c t dt ds s = s0 + v0t + 12 act 2 v = dt a ds = v dv v2 = v20 + 2ac(s - s0) Equations of Motion Particle F = ma 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 = 1mvG2 + 12IG v2 Particle Curvilinear Motion x, y, z Coordinates r, u, z Coordinates # ## # # ## ax = x vx = x Work a = r - ru2 v r = r # ## # r ## # # ay = y vy = y vu = r u a = r u + 2r u Variable force # vz = z ## # vz = z az = z u ## az = z n, t, b Coordinates # v = s Relative Motion vB = vA + vB/A dv # at = v = v ds [1 + (dy >dx)2]3>2 v2 r = an = r 0 d2y > dx2 0 aB = aA + aB/A Rigid Body Motion About a Fixed Axis Variable a Constant a = ac dv a = v = v0 + act dt du v = u = u0 + v0t + 12act 2 dt v dv = a du v2 = v20 + 2ac(u - u0) For Point P s = ur v = vr at = ar an = v2r Relative General Plane Motion—Translating Axes vB = vA + vB>A (pin) aB = aA + aB>A (pin) Relative General Plane Motion—Trans. and Rot. Axis vB = vA +  * rB>A + (vB>A )xyz # UF = F cos u ds L Constant force UF = (Fc cos u)  s Weight UW = - W y Spring Us = - 1 12 ks 22 - 12 ks 21 2 Couple moment UM = Mu Power and Efficiency Pout Uout dU = F#v P= e = = dt Pin Uin Conservation of Energy Theorem T1 + V 1 = T2 + V 2 Potential Energy V = V g + V e, where V g = {W y, V e = + 21 ks 2 Principle of Linear Impulse and Momentum Particle r2 dm L I = IG + md2 I k = Am Mass Moment of Inertia I = Parallel-Axis Theorem Radius of Gyration mv1 +  L F dt = mv2 F dt = m(vG)2 L Conservation of Linear Momentum  (syst. mv)1 =  (syst. mv)2 (vB)2 - (vA)2 e = Coefficient of Restitution (vA )1 - (vB )1 Principle of Angular Impulse and Momentum Rigid Body Particle aB = aA +  * rB>A +  * (  * rB>A ) + 2 * (vB>A )xyz + (aB>A )xyz KINETICS 2 m(vG)1 +  MO dt = (HO)2 L where HO = (d)(mv) (HO)1 +  MG dt = (HG)2 L where HG = IGv (HG)1 +  Rigid Body (Plane motion) MO dt = (HO)2 L where HO = IOv Conservation of Angular Momentum (syst. H)1 = (syst. H)2 (HO)1 + 