PCE MASTER EQUARTIONS

If UNED says circular orbit

Set gravitational force = centripetal force / G*M*m/r^2 = m*v^2/r

If UNED says satellite in circular orbit

Set gravitational force = centripetal force / G*M*m/r^2 = m*v^2/r

If UNED asks for orbital velocity

Set gravitational force = centripetal force / G*M*m/r^2 = m*v^2/r

If UNED asks for Kepler's Third Law derivation

Start with gravitational force = centripetal force

If UNED says charged particle moves in a circle inside a magnetic field

Set magnetic force = centripetal force / q*v*B = m*v^2/r

If UNED asks for radius of charged particle path

Set magnetic force = centripetal force / q*v*B = m*v^2/r

If UNED asks for mass of charged particle in magnetic field

Set magnetic force = centripetal force / q*v*B = m*v^2/r

If UNED says particle moves straight through crossed E and B fields

Set electric force = magnetic force / qE = qvB

If UNED says particle is not deflected

Set net force = 0 / electric force = magnetic force

If UNED asks for velocity selector

Set electric force = magnetic force / qE = qvB

If UNED says maximum height in projectile motion

Set final velocity = 0

If UNED says escape velocity

Set initial mechanical energy = final mechanical energy / Ei = Ef

If UNED says object barely escapes planet

Set final kinetic energy = 0

If UNED asks for stopping potential in photoelectric effect

Set kinetic energy = electric potential energy / Kmax = e*Vstop

If UNED asks whether photoelectrons are emitted

Compare photon energy and work function / Ephoton > phi

If UNED asks for photoelectron kinetic energy

Photon energy = work function + kinetic energy / Ephoton = phi + Kmax

If UNED asks for induced current direction

Use Lenz's Law / induced field opposes change in flux

If UNED asks for work in a conservative field

Set work = negative change in potential energy / W = -dU

If UNED asks for work done by electric field

Set work = charge times potential difference / W = q*dV

If UNED asks for work done by gravity

Set work = negative change in gravitational potential energy / W = -dU

If UNED asks for total mechanical energy

Set E = K + U

If UNED asks for conservation of mechanical energy

Set Ei = Ef

If UNED says no friction or losses

Set Ei = Ef

If UNED asks for orbital energy

Set E = K + U

If UNED asks for activity of radioactive sample

Set A = lambda*N

If UNED asks for radioactive time

Use decay equation and logarithms / unknown is in exponent

If UNED says half-life

Use N = N0*(1/2)^(t/T1/2)

If UNED asks for remaining mass

Use m = m0*(1/2)^(t/T1/2)

If UNED asks for electric field from several charges

Add fields using superposition

If UNED asks for electric potential from several charges

Add potentials using superposition

If UNED asks for magnetic field from several wires

Add fields vectorially using superposition

If UNED asks where total magnetic field is zero

Set B1 = B2

If UNED asks where total electric field is zero

Set E1 = E2

If UNED asks for image position in mirror or lens

Use 1/f = 1/s + 1/s'

If UNED asks for image size

Use magnification / m = -s'/s = h'/h

If UNED asks for critical angle

Set refracted angle = 90 degrees in Snell's Law

If UNED asks for total internal reflection

Use sin(thetac) = n2/n1

If UNED asks for refraction angle

Use n1*sin(theta1) = n2*sin(theta2)

If UNED asks for wave speed

Use v = f*lambda

If UNED gives wave equation and asks for wavelength

Set k = 2*pi/lambda

If UNED gives wave equation and asks for frequency

Set w = 2*pi*f

If UNED gives wave equation and asks for speed

Set v = w/k

If UNED asks for intensity at a different distance

Set I1*r1^2 = I2*r2^2

If UNED asks for sound level in decibels

Use beta = 10*log(I/I0)

If UNED asks for photon energy from wavelength

Use E = h*c/lambda

If UNED asks for photon energy from frequency

Use E = h*f

If UNED asks for wavelength of a particle

Use De Broglie equation / lambda = h/(m*v)

If UNED asks for energy transition between atomic levels

Use dE = h*f

If UNED asks for wavelength emitted by atom

Use lambda = h*c/dE

If UNED asks for relativistic energy

Use E = m*c^2

If UNED asks for mass defect energy

Use E = d*m*c^2

If UNED asks for symmetry at center of triangle or circle

Equal vectors cancel / net force = 0

If UNED asks for force at center of equilateral triangle with identical masses

Use symmetry / net force = 0

If UNED asks for force at center of symmetric charge distribution

Use symmetry / net force = 0

If UNED asks for gravitational field strength g at distance r from a planet

g = G*M/r^2 / Strength of gravitational field created by mass M

If UNED asks for gravitational force on a mass m

F = m*g /Force equals mass times field

If UNED asks for gravitational force between two masses

F = G*M*m/r^2 /Newton's Law of Gravitation

If UNED asks for gravitational potential

V = -G*M/r /Potential energy per unit mass

If UNED asks for gravitational potential energy

U = m*V = -G*M*m/r / Energy due to position in gravitational field

If UNED asks for work done by gravity

W = -dU /Gravity is a conservative force

If UNED asks for escape velocity

ve = sqrt(2*G*M/r) /Minimum speed needed to escape forever

If UNED asks for orbital velocity

v = sqrt(G*M/r) /Speed of circular orbit

If UNED asks for orbital period

T^2 = (4*pi^2*r^3)/(G*M) /Kepler's Third Law

If UNED asks for orbital radius from period

r = cuberoot[(G*M*T^2)/(4*pi^2)] / Rearranged Kepler's Law

If UNED asks for kinetic energy in orbit

K = G*M*m/(2*r) / Circular orbit only

If UNED asks for total mechanical energy in orbit

E = -G*M*m/(2*r) / Circular orbit only

If UNED asks for energy needed to move between orbits

dE = Ef - Ei / Change in orbital energy

If UNED asks for electric field created by a charge

E = k*q/r^2 / Electric field from point charge

If UNED asks for electric force on a charge

F = q*E / Force equals charge times field

If UNED asks for force between two charges

F = k*q1*q2/r^2 / Coulomb's Law

If UNED asks for electric potential

V = k*q/r / Potential from point charge

If UNED asks for electric potential energy

U = k*q1*q2/r / Energy stored between charges

If UNED asks for work from a potential difference

W = q*dV / Work done moving charge

If UNED asks for several charges

Add fields and potentials using superposition / Total equals sum of contributions

If UNED asks for magnetic field from straight wire

B = (u0*I)/(2*pi*r) / Field around long wire

If UNED asks for magnetic field from circular loop center

B = (u0*I)/(2*R) / Field at center of loop

If UNED asks for magnetic force on moving charge

F = q*v*B*sin(theta) / Lorentz Force

If UNED asks for direction of magnetic force

Use right-hand rule / Thumb=v, fingers=B, palm=F

If UNED asks for charged particle moving in circle

q*v*B = m*v^2/r / Magnetic force provides centripetal force

If UNED asks for orbit radius in magnetic field

r = m*v/(q*B) / Rearranged circular motion equation

If UNED asks for particle mass in magnetic field

m = q*B*r/v / Rearranged circular motion equation

If UNED says particle is not deflected

qE = qvB / Electric force cancels magnetic force

If UNED asks for electric field in velocity selector

E = v*B / Straight-line motion condition

If UNED asks for force between parallel wires

F/L = (u0*I1*I2)/(2*pi*d) / Force per unit length

If UNED asks for magnetic flux

Phi = B*A*cos(theta) / Magnetic field passing through area

If UNED asks for induced emf

emf = -d(Phi)/dt / Faraday's Law

If UNED asks for current direction from induction

Use Lenz's Law / Opposes flux change

If UNED asks for wavelength

lambda = v/f / Wave equation

If UNED asks for frequency

f = v/lambda / Rearranged wave equation

If UNED asks for wave speed

v = f*lambda / Fundamental wave equation

If UNED gives wave equation y(x,t)=A*sin(wt-kx)

A = amplitude / Maximum displacement

If UNED gives wave equation

k = 2*pi/lambda / Wave number

If UNED gives wave equation

w = 2*pi*f / Angular frequency

If UNED gives wave equation

v = w/k / Wave speed

If UNED asks for intensity

I = P/A / Power per area

If UNED asks for intensity at another distance

I1*r1^2 = I2*r2^2 / Spherical wave spreading

If UNED asks for sound level

beta = 10*log(I/I0) / Decibel equation

If UNED asks for Doppler effect

f' = f*(v+/-vo)/(v-/+vs) / Observed frequency

If UNED asks for refractive index

n = c/v / Light slows in medium

If UNED asks for light speed in medium

v = c/n / Rearranged refractive index