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Formulas and Units

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Question
Answer
Velocity - acceleration is constant   vf = vi + a t  
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Linear Displacement - acceleration constant   xf = vi t + 1/2 a t2  
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Final Velocity   vf2 = vi2 + 2aΔx  
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Velocity Units   m/s or cm/s  
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Velocity Formula   Δx/Δt=V  
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Displacement formula   Δx = xf-xi  
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Vector x formula   Fx = F cosӨ  
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Vector y formula   Fy = F sinӨ  
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How to find Ө using x and y   Ө= tan–1(Fy/Fx)  
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Gravitational Formula   FG = GmM/r2  
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Momentum Conservation Formula   m1v1 + m2v2= m1v1 + m2v2 (Elastic collisions)  
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Power Formula   P=w/t  
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Angular Momentum Formula   L = mvr= Iw L =angular momentum, m =mass of the small object m1v1 + m2v2 v =magnitude of object’s velocity r = separation between the objects  
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Centripetal Force Formula   F=mv2/r  
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Work formula   W = F d cosӨ W= -μkmgΔx W= TΔxcosӨ W = PΔt  
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Kinetic Energy Formula   KE = ½ mv2 ΔKE = fkd energy lost  
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Potential Energy Formula   PE = mgh (gravitational)  
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Formula for gravity (general)   gravity (general): GmM/r  
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Spring Formula - Potential Energy   PE = ½ kx2 (x from equilibrium)  
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Heat Formula   Q= cmΔT c=heat capacity of substance m=mass of substance Q=Quantity of heat  
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Change in energy formula   ΔE = Q + W W=work E=entropy  
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Simple Machine Formula - lever   Torque = lever arm x force  
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Spring Periodic Motion Formula   T=2π (SQRroot m/k)  
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Pendulum Formula   T=2π (SQRroot L/g)  
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Period of object   period = 1/frequency  
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Coulomb’s Law   Fc = kqQ/r2 FC (force between q and Q)  
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Force felt by Q formula   F = QE (actual force felt by Q)  
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Ohmas Law   VR = IR (VR = resistor’s voltage drop)  
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Series Resisters Formula   Rt = R1 + R2  
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Parallel Resisters Formula   Rt= (1/R1 + 1/R2)–1  
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Power Lost by each resister   PR = IR 2R = VR 2/R  
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Circular Motion   X = R Cos Ө Y = R Sin Ө  
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Circular Motion Velocity   V = 2πr/T V = SqRoot g R TAN Ө  
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Period Formula   T = mg/CosӨ T = mV2/R  
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Moon Gravity   1/6 that of Earth  
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Weight Formula   W = mg  
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Distance for planets   d = D/(sqroot moon/M of earth) +1  
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Newton's 3rd Law Formula   Fab = -Fba = W  
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Tension Formula   T - Fg = (Fg/g) a EF = T-Fg = ma  
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Acceleration with Tension   a = g(F-Fg)/Fg) a = g sin Ө N = -mg Cos Ө  
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Freefall formula Drop   Drop = Viy/(G/2)  
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Freefall formula Range   Range = (v2/g) sin 2V or d= 1/2 gt2 Max at 45 degrees  
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Projectile Formula X component   Vxf = Vxi Vf = Xi+VixΔt Vfx2 = vix2  
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Projectile Formula y component   Vfy=Viy+2yΔt Yf = ViyΔt+1/2ay(Δt)2 Vfy2 = Viy2 + 2ayΔy  
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Projectile speed formula   Speed = sqroot Vx2+Vy2  
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Friction Formula Kinetic   fk = μk N  
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Friction Formula Static   Fs < μsN  
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Friction acceleration Formulas   a = -μkgCos Ө + g Sin Ө  
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Drag Force formula   F draV2 Vr = Sqroot (2mg/CpA)  
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Terminal Velocity Formula   Vt = sqroot 2mg/CpA  
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Hook's Law (springs)   F = -kx  
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Work on a spring   Wspring = (kx2/2) - (kxi/2)  
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Power Formula   P = FV P (mgh)/(Δt)  
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Average Power Formula   Avg P = W/Δt  
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Power Units   J/s = 1W Joules per second = Watt 1 hp = 746 Watts  
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Earth Data   6 X 10 24 Kg Radius 6 X 10 6 m  
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Univeral Gravitational Potential Energy   Ugrav = mgy ΔUgrav Ugrav = mg (d+h) mg (yf-yi)  
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Mechanical Energy   KE+PE = E  
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Four Forces   Gravity Electrical Magnetism Strong Nuclear Force Weak Nuclear Force  
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Kepler's Formula   T2/r3  
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Orbital Motion   V = sqroot Gm/r satellite speed T2 = (4π2/Gm)r3  
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Momentum Formula   ρ = mv Angular Momentum (ω)  
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Rotational Inertia Formula   Rotational Inertia = mr2  
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Impulse formula   I = Ft I = Δp I = pf=pi change momentum F= Δp/Δt If no net force Δp = 0  
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Elastic Collision formulas   Vif = (m1-m2/m1+m2) Vi V2f = (2mi/m1+m2)Vi Δp = 0 ΔE =0  
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Inelastic collisions   h = 1/2 (m1+m2)Vf2/(m1+m2)g ΔP = 0 E not conserved  
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Harmonic Motion   1/2kx2=1/2mv2 (pedulum)  
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Restore Force   ԐF = -kx restore ԐF = -k-x compression  
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Spring Acceleration   a = (k/m)x  
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Tangential SPeed   V = rω V = sqroot ((kx)/m )  
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Potential Inertia -Pendulum   l = mv2  
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Potential Inertia - Hoop   l= 1/2mr2  
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Radian Measures   s/r =Ө or C=2πr s = arc length 1/2 circle = S= 1/2C = 180 degrees s/r = π 2π/360 = 1, 180= S/R = π, 90 = S = 1/4C, S = (30/60)C = 1/12, 360 = 2π  
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Center of Mass - Centripetal Force   F = mvr2/r  
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Linear Momentum   linear momentum = mv  
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angular momentum   angular momentum = mvr  
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Center of Mass   rcm = (m1r1+m2r2)/(m1+m2)  
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Revolution or cycle   n = S/C = S/(2πr)  
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Angular Velocity (ω)   ω= 2πf ω = r(ΔӨ/Δt) V = rω  
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Angular Velocity (ω) Units   1/s or s-1 Hertz (Hz) = 1s-1 radian /s  
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Acceleration - using angular   a = v2/r a =rω2  
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Force Normal - angular   FN = mg = Mrω2 ω = sqroot (g/r)  
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Revolution   T = period = 1 Revolution 1 rad/s = 9.55 r/min = 0.159 r/s  
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Torque   Ft=Mat = Mrα F = T r = R a = Iω  
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Moment of Inertia   I = mr2  
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Rotational KE   KErot = 1/2Iω 2 KEtot = KEin+KEout = 1/2mV2+1/2Iω2 K = 1/2lω2 KE=1/2m(Rw)2 = circle  
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Angular Momentum   L =r(perpendicular)mv  
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Aphelion   V = r(perpendicular) ω Tangential SPeed V = rω Orbit speed  
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