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Physics Crib Sheet 5 - Formulae Used in Physics
v = s / t{velocity} = {distance} / {time}
F = m . a{force} = {mass} . {acceleration}
W = m . g{weight} = {mass} . {gravitational acceleration}
v = u + (a . t){velocity} = {initial velocity} + ({acceleration} . {time})
v2 = u2 + (2 . a . s){final velocity}2 = {initial velocity}2 + (2 . {acceleration} . {distance})
s = (u . t) + (½ . a . t2){distance} = ({initial velocity} . {time}) + (½ . {acceleration} . {time}2)
s = ½ (u + v) . t{distance} = ½ ({initial velocity} + {final velocity}) . {time}
p = m . v{momentum} = {mass} . {velocity}
µ = F / R{coefficient of friction} = {force} / {resistance}
µ' = F' / R{coefficient of sliding friction} = {sliding force} / {resistance}
µ = tan(θ){coefficient of friction} = tan({angle})
T = F . r{torque} = {force} . {radius of curvature}
ω = θ / t{angular velocity} = {angle} / {time}
T = (2 . π) / ω{period} = (2 . {pi}) / {angular velocity}
v = r . ω{velocity} = {radius of curvature} . {angular velocity}
a = ω2 . r{angular acceleration} = {angular velocity}2 . {radius of curvature}
tan(θ) = v2 / (g . r)tan({angle}) = {velocity}2 / ({gravitational acceleration} . {radius of curvature})
KErot = ½ I . ω2{rotational kinetic energy} = ½ {moment of inertia} . {angular velocity}2
p = I . ω{angular momentum} = {moment of inertia} . {angular velocity}
T = I . a{torque} = {moment of inertia} . {angular acceleration}
ω = ω + a . t{angular velocity} = {initial angular velocity} + {angular acceleration} . {time}
ω2 = ω2 + (2 . a . θ){angular velocity}2 = {initial angular velocity}2 + (2 . {angular acceleration} . {angle})
θ = ω . t + (½ . a . t2){angle} = {initial angular velocity} . {time} + (½ . {angular acceleration} . {time}2)
θ = ½ . (ω + ω) . t{angle} = ½ . ({initial angular velocity} + {angular velocity}) . {time}
W = T . θ{work} = {torque} . {angle}
W = F . s{work} = {force} . {distance}
KE = ½ . m . v2{kinetic energy} = ½ . {mass} . {velocity}2
PE = m . g . h{potential energy} = {mass} . {gravitational acceleration} . {height}
v = (2 . g . h)½{velocity} = (2 . {gravitational acceleration} . {height})½
P = W / t{power} = {work} / {time}
P = F . v{power} = {force} . {velocity}
v = ±ω . (a - s)½{velocity} = {plusminus}{angular velocity} . ({angular acceleration} - {distance})½
s = a . cos(ω . t){distance} = {angular acceleration} . cos({angular velocity} . {time})
s = a . cos( (ω . t) + ε){distance} = {angular acceleration} . cos( ({angular velocity} . {time}) + {initial phase angle})
T = (2 . π) / ω{period} = (2 . {pi}) / {angular velocity}
T = 2 . π . (m/k)½{period} = 2 . {pi} . ({mass}/{stiffness constant})½
F = (G . m1 . m2) / s2{force} = ({universal gravitational constant} . {mass}1 . {mass}2) / {distance}2
ve = ( (2 . G . mE) / rE)½{escape velocity} = ( (2 . {universal gravitational constant} . {mass of earth}) / {radius of earth})½
E = Ts / Tst{Youngs modulus} = {tensile stress} / {tensile strain}
W = (E . A . e) / (2 . L){work} = ({Youngs modulus} . {area} . {extension}) / (2 . {original length})
p . V = n . R . θ{pressure} . {volume} = {number of moles} . {gas constant} . {temperature}
n = c / cmat{refractive index} = {speed of light} / {speed of light in material}
n1 . sin1) = n2 . sin2){refractive index}1 . sin ({angle}1) = {refractive index}2 . sin ({angle}2)
(1 / f) = (1 / f1) + (1 / f1) + ...(1 / {focal length}) = (1 / {focal length}1) + (1 / {focal length}1) + ...
f = 1 / T{frequency} = 1 / {period}
fB = f1 - f2{beat frequency} = {frequency}1 - {frequency}2
f = (n / (2 . ls)) . (T / µ)½{frequency} = ({harmonic number} / (2 . {string length})) . ({period} / {mass per unit length})½
I = Q . t{current} = {charge} . {time}
R = V / I{resistance} = {voltage} / {current}
R = (ρ . l) / A{resistance} = ({resistivity} . {length}) / {area}
G = 1 / R{conductance} = 1 / {resistance}
σ = 1 / ρ{conductivity} = 1 / {resistivity}
J = I / A{current density} = {current} / {area}
E = E1 + E2 + ...{electromotive force} = {electromotive force}1 + {electromotive force}2 + ...
Rs = R1 + R1 ...{series resistance} = {resistance}1 + {resistance}1 ...
(1/Rp) = (1/R1) + (1/R1) ...(1/{parallel resistance}) = (1/{resistance}1) + (1/{resistance}1) ...
P = V . I{power} = {voltage} . {current}
P = V2 / R{power} = {voltage}2 / {resistance}
P = I2 . R{power} = {current}2 . {resistance}
F = (1 / (4 . π . ε0 . εr) ) . ( Q1 . (( Q2 ) / r2){force} = (1 / (4 . {pi} . {permittivity of free space} . {relative permittivity}) ) . ( {charge}1 . (( {charge}2 ) / {separation}2)
E = (1 / (4 . π . ε0 . εr) ) . (Q / r2){electric field strength} = (1 / (4 . {pi} . {permittivity of free space} . {relative permittivity}) ) . ({charge} / {separation}2)
V = (1 / (4 . π . ε0 . εr) ) . (Q / r){voltage} = (1 / (4 . {pi} . {permittivity of free space} . {relative permittivity}) ) . ({charge} / {separation})
W = Q . V{work} = {charge} . {voltage}
E = V / r{electric field strength} = {voltage} / {separation}
C = Q / V{capacitance} = {charge} / {voltage}
C = (ε0 . εr . A) / r{capacitance} = ({permittivity of free space} . {relative permittivity} . {area}) / {separation}
(1 / Cs) = (1 / C1) + (1 / C2) + ...(1 / {series capacitance}) = (1 / {capacitance}1) + (1 / {capacitance}2) + ...
Cp = C1 + C2 ...{parallel capacitance} = {capacitance}1 + {capacitance}2 ...
V = V0 . e(-t/(C . R)){voltage} = {initial voltage} . e(-{time}/({capacitance} . {resistance}))
Ψ = A . B . cos(θ){electric flux} = {area} . {magnetic field strength} . cos({angle})
B = (µ0 . µr . I) / (2 . π . s){magnetic field strength} = ({permeability of free space} . {relative permeability} . {current}) / (2 . {pi} . {distance})
Bs = (µ0 . µr . N . I{magnetic field strength long solenoid} = ({permeability of free space} . {relative permeability} . {number of turns} . {current}
F = B . I . l . sin(θ){force} = {magnetic field strength} . {current} . {length} . sin({angle})
F = B . Q . v . sin(θ){force} = {magnetic field strength} . {charge} . {velocity} . sin({angle})
F = (µ0 . µr . I1 . I2 . l) / (2 . π . r){force} = ({permeability of free space} . {relative permeability} . {current}1 . {current}2 . {length}) / (2 . {pi} . {separation})
V = VMAX . sin((f . t) / (2 . π){voltage} = {maximum voltage} . sin (({frequency} . {time}) / (2 . {pi})
I = Io . sin((f . t) / (2 . π){current} = {maximum current} . sin (({frequency} . {time}) / (2 . {pi})
VRMS = VMAX / 2½{RMS voltage} = {maximum voltage} / 2½
IRMS = Io / 2½{RMS current} = {maximum current} / 2½
X = VMAX / Io{reactance} = {maximum voltage} / {maximum current}
X = VRMS / IRMS{reactance} = {RMS voltage} / {RMS current}
f = 1 / (2 . π . (L . C)½){frequency} = 1 / (2 . {pi} . ({inductance} . {capacitance})½)
F = NA . e{Faraday constant} = {Avogadros number} . {electron charge}
E = h . f{energy} = {Plancks constant} . {frequency}
E = h . c / λ{energy} = {Plancks constant} . {speed of light} / {wavelength}
λ = h / (mr . v){wavelength} = {Plancks constant} / ({relative mass} . {velocity})
N = N0 . e-λt{number of atoms} = {initial number of atoms} . {e}-{decay constant}{time}
T½ = (loge(2)) / λ{halflife} = (loge(2)) / {decay constant}
E = m . c2{energy} = {mass} . {speed of light}2
A = π . r2{area} = {pi} . {radius}2
C = 2 . π . r{circumference} = 2 . {pi} . {radius}
A = 4 . π . r2{area} = 4 . {pi} . {radius}2
V = (4 / 3) . π . r3{volume} = (4 / 3) . {pi} . {radius}3
m = mo . ( 1 - ( v2 / c2 ) ){mass} = {rest mass} . ( (1 - ( {velocity}2 / {speed of light}2 ) )
t = to . ( 1 - ( v2 / c2 ) ){static time} = {moving time} . ( (1 - ( {velocity}2 / {speed of light}2 ) )
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