Formula Cheat Sheet Physics - Mechanics | University of Illinois at Urbana-Champaign

University:
University of Illinois at Urbana-Champaign
Course:
PHYS 211 | University Physics: Mechanics
Academic year:

2023
Views:

214

Pages:

1
Author:

Ronnie Haynes

Formula Sheet Kinematics v = v0 + at r = r0 + v0t + at2/2 v2 = v02 + 2a(x-x0) g = 9.81 m/s2 = 32.2 ft/s2 vA,B = vA,C + vC,B Uniform Circular Motion a = v2/r = 2r v = r  = 2/T = 2f Dynamics Fnet = ma = dp/dt FA,B = -FB,A F = mg (near earth's surface) F12 = -Gm1m2/r2 (in general) (where G = 6.67x10-11 Nm2/kg2) Fspring = - k x Friction f = kN (kinetic) f  SN (static) Work & Kinetic energy W =  F dl W = F  r = F r cos (constant force) Wgrav = -mgy Wspring = - k(x2 2 - x12)/2 K = mv2/2 = p2/2m WNET = K Potential Energy Ugrav = mgy (near earth surface) Ugrav = -GMm/r (in general) Uspring = kx2/2 E = K + U = Wnc Power P = dW/dt P = Fv (for constant force) System of Particles RCM = miri / mi VCM = mivi / mi ACM = miai / mi P = mivi FEXT = MACM = dP/dt Impulse I =  F dt P = Favt Simple Harmonic Motion: d2x/dt2 = -2x (differential equation for SHM) Collisions: If FEXT = 0 in some direction, then Pbefore = Pafter in this direction: mivi (before) = mivi (after) x(t) = Acos(t + ) v(t) = -Asin(t + ) a(t) = -2Acos(t + ) In addition, if the collision is elastic: * Ebefore = Eafter * Rate of approach = Rate of recession * The speed of an object in the Center-of-Mass reference frame is unchanged by an elastic collision. Rotational kinematics s = R, v = R, a = R  = 0 +  0 t + 1/2 t2  = 0 + t  = 02 + 2 Rotational Dynamics I = miri 2 Iparallel = ICM + MD2 Idisk = Icylinder = 1/2MR2 Ihoop = MR2 Isolid-sphere = 2/5MR2 Ispherical shell = 2/3MR2 Irod-cm = 1/12ML2 Irod-end = 1/3 ML2  = I(rotation about a fixed axis) r x F , rFsin Work & Energy Krotation = 1/2I2 , Ktranslation = 1/2MVcm 2 Ktotal = Krotation + Ktranslation W =  Statics F = 0 ,  = 0 (about any axis) Angular Momentum: L=rxp Lz = Iz Ltot = LCM + L* ext = dL/dt cm = dL*/dt precession =  / L 2 = k/m (mass on spring) 2 = g/L (simple pendulum) 2 = mgRCM/I (physical pendulum) 2 = /I (torsion pendulum) General harmonic transverse waves: y(x,t) = Acos(kx -t) k = 2/,  = 2f = 2/T v = f = /k Waves on a string: v2  F   tension mass per unit length  1 v 2 A2 2 dE 1   2 A 2 dx 2 d2 y 1 d 2y  2 2 Wave Equation 2 dx v dt P Fluids:  m V p F A A1v1  A2v2 p1  21 v12   gy1  p 2  21 v 22   gy 2 FB   liquid gVliquid F2  F1 A2 A1

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