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Big Five Equations
Missing a d = ½(vO + v)t
Missing v d= vot + ½at^2
Missing vo d = vt – ½at^2
Missing d v = vot + at
Missing t v^2 = vo^2 + 2ad
If vo is at an angle θ
vox
voy
vox = vo cosθ
voy = vo sinθ
Newton’s Law of Gravitation
Fg = GMm / r^2
G = 6.7e-11
Force of Friction
Ff = μFn
Object on an incline plane, what is
Fg
Fn
Fg = mgsin θ (weight parallel to ramp)
Fn = mgcos θ (weight perpendicular to ramp)
Center of mass for point masses
X = (m1x1 + m2x2 + m3x3) / (m1 + m2 + m3)
Center of gravity
X = (w1x1 + w2x2 + w3x3) / (w1 + w2 + w3)
similar to center of mass, but gravity is also used
Centripetal acceleration/force
Ac = v^2 / r
Fc = mv^2 /r
Torque
τ = rFsin θ = rFsin θ’ = LF
measured in N•m
Rotational Inertia/moment of intertia
τ = Iα
Work
W = Fdcos θ = Pt
Measured in J
Power
P = Work/time = W/t = Fd/t = Fv
Mechanical Advantage
MA = Effort distance/resistance distance
Efficiency
Efficiency = Woutput/Einput (%)
Momentum
P = mv
Impulse-momentum theorem
J = Δp = FΔt
Angular momentum
L = lmv = Iw
Density
Density = mass/volume = m/v
Specific gravity
s.g. = px / pH2O
pH2O = 1000 kg/m^3 or 1 g/cm^3
Force of gravity on fluids
Given p = m/V
Fg = mg = pVg
Pressure/Hydrostatic gauge pressure
P = F(perpindicular)/Area
P = Wfluid/A = pf Vf g /A = pf A D g / A = pf D g
Buoyant force
Fb = pf Vsub g

If at equilibrium
Vsub / V = pobject / pfluid
Pascal’s law
F1/A1 = F2/A2
F2 = A2F1 / A2
Surface tension
ϒ = F/2L
ϒ is coefficient of surface tension
Flow rate
f=av
Bernouli effect
When speed increases, pressure is lowered
Stress
Magnitude of force over an area
Stress = F/A
Strain
Change in length of object stressed
Tensile/compressive – Strain = ΔL / Lo
Shear – Strain = Distance of shear / Lo = X / Lo
Hooke’s law of Stress/Strain
Stress = Modulus x Strain
Tension/compressive – ΔL = FLo / EA
Shear
Coulomb’s Law
Fe = kqq / r^2
k = 9e9
Electric field equations
E = KQ / r^2
Fe = KQq / r^2 = Eq
Electric Potential
Φ = KQ / r
Change in Potential Energy
ΔPE = qΔΦ = qV
Work done by E field
W(by E field) = -ΔPEelec
ΔKE = -ΔPE
Current
I = Q/t
Measured in amps (charge/second)
Resistance
V = IR
R = pL/ A
Measured in Ohms
Power (Electrical)
P = IV = I^2 / R = V^2 / R
Measured in Watts (work/time)
Charge on a capacitor
Q = C/V
Measured in Farads (charge/voltage)
Capacitance on a parallel plate capacitator
C = εoA / d
C = KεoA / d (with dielectric)
Εo = 1 / 4πk = 8.85e-12 F/m
Ed’s formula
V = Ed
Potential energy
PE = mgh = ½QV
RMS voltage and current
Vrms = Vmax / √2
Irms = Imax / √2
Magnetic force
Fb = q (v x B) = |q|vBsinθ
Right hand rule
For positive charges
Thumb – direction of V
Palm – direction of Fb
Fingers – direction of B

For current in a wire
Thumb – direction of I
Fingers – direction of B
Magnetic field for a solenoid
B α IN / L
Hooke’s law
F = -kx
k is spring constant
Elastic potential energy
PE = -½kx^2
Period
Time it takes for one round trip of simple harmonic motion
T = 1 / f
T = 2π √ (l / g)
Measured in seconds
Frequency
Number of cycles in one second
F = 1 / T
F = 1 / 2π √(g / l)
Measured in Hz
Wave equation
v = λf
v = √ (tension / linear density)
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