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Formulas and Units

Velocity - acceleration is constant vf = vi + a t
Linear Displacement - acceleration constant xf = vi t + 1/2 a t2
Final Velocity vf2 = vi2 + 2aΔx
Velocity Units m/s or cm/s
Velocity Formula Δx/Δt=V
Displacement formula Δx = xf-xi
Vector x formula Fx = F cosӨ
Vector y formula Fy = F sinӨ
How to find Ө using x and y Ө= tan–1(Fy/Fx)
Gravitational Formula FG = GmM/r2
Momentum Conservation Formula m1v1 + m2v2= m1v1 + m2v2 (Elastic collisions)
Power Formula P=w/t
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
Centripetal Force Formula F=mv2/r
Work formula W = F d cosӨ W= -μkmgΔx W= TΔxcosӨ W = PΔt
Kinetic Energy Formula KE = ½ mv2 ΔKE = fkd energy lost
Potential Energy Formula PE = mgh (gravitational)
Formula for gravity (general) gravity (general): GmM/r
Spring Formula - Potential Energy PE = ½ kx2 (x from equilibrium)
Heat Formula Q= cmΔT c=heat capacity of substance m=mass of substance Q=Quantity of heat
Change in energy formula ΔE = Q + W W=work E=entropy
Simple Machine Formula - lever Torque = lever arm x force
Spring Periodic Motion Formula T=2π (SQRroot m/k)
Pendulum Formula T=2π (SQRroot L/g)
Period of object period = 1/frequency
Coulomb’s Law Fc = kqQ/r2 FC (force between q and Q)
Force felt by Q formula F = QE (actual force felt by Q)
Ohmas Law VR = IR (VR = resistor’s voltage drop)
Series Resisters Formula Rt = R1 + R2
Parallel Resisters Formula Rt= (1/R1 + 1/R2)–1
Power Lost by each resister PR = IR 2R = VR 2/R
Circular Motion X = R Cos Ө Y = R Sin Ө
Circular Motion Velocity V = 2πr/T V = SqRoot g R TAN Ө
Period Formula T = mg/CosӨ T = mV2/R
Moon Gravity 1/6 that of Earth
Weight Formula W = mg
Distance for planets d = D/(sqroot moon/M of earth) +1
Newton's 3rd Law Formula Fab = -Fba = W
Tension Formula T - Fg = (Fg/g) a EF = T-Fg = ma
Acceleration with Tension a = g(F-Fg)/Fg) a = g sin Ө N = -mg Cos Ө
Freefall formula Drop Drop = Viy/(G/2)
Freefall formula Range Range = (v2/g) sin 2V or d= 1/2 gt2 Max at 45 degrees
Projectile Formula X component Vxf = Vxi Vf = Xi+VixΔt Vfx2 = vix2
Projectile Formula y component Vfy=Viy+2yΔt Yf = ViyΔt+1/2ay(Δt)2 Vfy2 = Viy2 + 2ayΔy
Projectile speed formula Speed = sqroot Vx2+Vy2
Friction Formula Kinetic fk = μk N
Friction Formula Static Fs < μsN
Friction acceleration Formulas a = -μkgCos Ө + g Sin Ө
Drag Force formula F draV2 Vr = Sqroot (2mg/CpA)
Terminal Velocity Formula Vt = sqroot 2mg/CpA
Hook's Law (springs) F = -kx
Work on a spring Wspring = (kx2/2) - (kxi/2)
Power Formula P = FV P (mgh)/(Δt)
Average Power Formula Avg P = W/Δt
Power Units J/s = 1W Joules per second = Watt 1 hp = 746 Watts
Earth Data 6 X 10 24 Kg Radius 6 X 10 6 m
Univeral Gravitational Potential Energy Ugrav = mgy ΔUgrav Ugrav = mg (d+h) mg (yf-yi)
Mechanical Energy KE+PE = E
Four Forces Gravity Electrical Magnetism Strong Nuclear Force Weak Nuclear Force
Kepler's Formula T2/r3
Orbital Motion V = sqroot Gm/r satellite speed T2 = (4π2/Gm)r3
Momentum Formula ρ = mv Angular Momentum (ω)
Rotational Inertia Formula Rotational Inertia = mr2
Impulse formula I = Ft I = Δp I = pf=pi change momentum F= Δp/Δt If no net force Δp = 0
Elastic Collision formulas Vif = (m1-m2/m1+m2) Vi V2f = (2mi/m1+m2)Vi Δp = 0 ΔE =0
Inelastic collisions h = 1/2 (m1+m2)Vf2/(m1+m2)g ΔP = 0 E not conserved
Harmonic Motion 1/2kx2=1/2mv2 (pedulum)
Restore Force ԐF = -kx restore ԐF = -k-x compression
Spring Acceleration a = (k/m)x
Tangential SPeed V = rω V = sqroot ((kx)/m )
Potential Inertia -Pendulum l = mv2
Potential Inertia - Hoop l= 1/2mr2
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
Center of Mass - Centripetal Force F = mvr2/r
Linear Momentum linear momentum = mv
angular momentum angular momentum = mvr
Center of Mass rcm = (m1r1+m2r2)/(m1+m2)
Revolution or cycle n = S/C = S/(2πr)
Angular Velocity (ω) ω= 2πf ω = r(ΔӨ/Δt) V = rω
Angular Velocity (ω) Units 1/s or s-1 Hertz (Hz) = 1s-1 radian /s
Acceleration - using angular a = v2/r a =rω2
Force Normal - angular FN = mg = Mrω2 ω = sqroot (g/r)
Revolution T = period = 1 Revolution 1 rad/s = 9.55 r/min = 0.159 r/s
Torque Ft=Mat = Mrα F = T r = R a = Iω
Moment of Inertia I = mr2
Rotational KE KErot = 1/2Iω 2 KEtot = KEin+KEout = 1/2mV2+1/2Iω2 K = 1/2lω2 KE=1/2m(Rw)2 = circle
Angular Momentum L =r(perpendicular)mv
Aphelion V = r(perpendicular) ω Tangential SPeed V = rω Orbit speed
Created by: pheinen3