Formulas and Units
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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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