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Physics 1 Equations

$v_{xf}\;=\;v_{xi}\;+\;a_{x}t$	Velocity as a function of time
$x_{f}\;=\;x_{i}\;+\;{\frac {1}{2}}\left(v_{xi}\;+\;v_{xf}\right)t$	Position as a function of velocity and time
$x_{f}\;=\;x_{i}\;+\;v_{xi}t\;+\;{\frac {1}{2}}a_{x}t^{2}$	Position as a function of time
$v_{xf}^{2}\;=\;v_{xi}^{2}\;+\;2a_{x}\left(x_{f}\;-\;x_{i}\right)$	Velocity as a function of position
$x_{f}\;=\;x_{i}\;+\;v_{xi}t\;+\;{\frac {1}{2}}a_{x}t^{2}$	x-dimension of particle with constant acceleration
$y_{f}\;=\;y_{i}\;+\;v_{yi}t\;+\;{\frac {1}{2}}a_{y}t^{2}$	y-dimension of particle with constant acceleration
$h={\frac {v_{i}^{2}\;\sin ^{2}\theta _{i}}{2g}}$	Maximum height of a projectile
$R={\frac {v_{i}^{2}\;\sin \;2\theta _{i}}{g}}$	Horizontal range of a projectile
$a_{c}\;=\;{\frac {v^{2}}{r}}$	Centripetal (center-seeking) acceleration
$T\;=\;{\frac {2\pi r}{v}}$	Period of circular motion
$a_{r}\;=\;-a_{c}$	Radial acceleration
$f_{k}\;=\;\mu _{k}n$	Magnitude of force of kinetic friction
$W\;\equiv \;F\;\Delta r\;\cos \theta$	The amount of work done on a system
$K\;\equiv \;\;{\frac {1}{2}}mv^{2}$	Kinetic energy of a particle
$U_{g}\;\equiv \;mgy$	Gravitational potential energy
$U_{s}\;\equiv \;{\frac {1}{2}}kx^{2}$	Elastic potential energy
$K_{f}\;+\;U_{f}\;=\;K_{i}\;+\;U_{i}\;=\;{\frac {1}{2}}mv_{f}^{2}\;+\;mgy_{f}\;={\frac {1}{2}}mv_{i}^{2}\;+\;mgy_{i}$	Isolated model system

Physics 2 Equations

Exam 1

$F_{e}\;=\;k_{e}{\frac {\left\|q_{1}\right\|\left\|q_{2}\right\|}{r^{2}}}$	Coulomb's law
$a\;=\;{\frac {q{\mbox{E}}}{m}}$	Acceleration of a particle in a uniform electric field
$\Phi _{\mbox{E}}\;=\;{\mbox{E}}A\;\cos \;\theta$	Electric flux through a surface of fixed area
$\Phi _{\mbox{E}}\;=\;4\pi k_{e}q$	Electric flux through a gaussian sphere
$\Phi _{\mbox{E}}\;=\;{\frac {q_{in}}{\epsilon _{0}}}$	Gauss's Law
${\mbox{E}}\;=\;k_{e}{\frac {Q}{r^{2}}}$	Electric field at a point outside an insulating solid sphere with uniform charge density
${\mbox{E}}\;=\;k_{e}{\frac {Q}{a^{3}}}r$	Electric field at a point inside an insulating solid sphere with uniform charge density
$q_{in}\;=\;\sigma A$	Charge from surface charge density and area
${\mbox{E}}\;=\;{\frac {\sigma }{\epsilon _{0}}}$	Electric field from surface charge density
$\Delta U\;=\;q_{0}\;\Delta V$	The change in potential energy of a charge-field system
$V\;=\;k_{e}\sum _{i}^{}{\frac {q_{i}}{r_{i}}}$	Electric potential due to several point charges
${\mbox{C}}\;\equiv \;{\frac {Q}{\Delta V}}$	Capacitance
$\Delta V\;=\;{\mbox{E}}d\;=\;{\frac {Qd}{\epsilon _{0}A}}$	Potential between parallel plates
${\mbox{C}}_{eq}\;=\;{\mbox{C}}_{1}\;+\;{\mbox{C}}_{2}\;+\;...$	Capacitors in parallel
${\frac {1}{{\mbox{C}}_{eq}}}\;=\;{\frac {1}{{\mbox{C}}_{1}}}\;+\;{\frac {1}{{\mbox{C}}_{2}}}\;+\;...$	Capacitors in series
$R\;=\;\rho \;{\frac {l}{A}}$	Resistance of a uniform material along length
$R\;\equiv \;{\frac {\Delta V}{I}}$	Resistance as a ratio of potential difference to the current
$I\;=\;{\frac {\epsilon }{R\;+\;r}}$	Current in terms of emf and load resistance
$R_{eq}\;=\;R_{1}\;+\;R_{2}\;+\;...$	Resistors in series
${\frac {1}{R_{eq}}}\;=\;{\frac {1}{R_{1}}}\;+\;{\frac {1}{R_{2}}}\;+\;...$	Resistors in parallel
${\mathcal {P}}\;=\;I\Delta V$	Power in terms of potential difference and current
$F_{B}\;=\;\left\|q\right\|vB\sin \theta$	Magnetic force on a charged particle moving in a magnetic field
$K\;=\;{\frac {1}{2}}mv^{2}\;=\;{\frac {q^{2}B^{2}R^{2}}{2m}}$	Kinetic energy of an ion in a cyclotron
$\tau _{\max }\;=\;NIAB\sin \theta$	Torque on a current loop in a magnetic field

Exam 2

$\mu _{0}\;=\;4\pi \;\times \;10^{-7}\;{\frac {T\cdot m}{A}}$	Permeability of free space.
$B\;=\;{\frac {\mu _{0}I}{2\pi a}}$	Magnetic field of any straight current-carrying wire.
$B\;=\;{\frac {\mu _{0}I}{2a}}$	Magnetic field at the center of a wire loop.
$F\;=\;IlB$	Magnetic force on a length of wire.
$F_{B}\;=\;{\frac {\mu _{0}I_{1}I_{2}}{2\pi a}}$	The force between two parallel wires.
$B\;=\;{\frac {\mu _{0}NI}{2\pi r}}$	Magnetic field of a torus.
$B\;=\;\mu _{0}{\frac {N}{l}}I$	Magnetic field inside a solenoid.
$\left\|\epsilon \right\|\;=\;N{\frac {\Delta \left(BA\right)}{\Delta t}}$	Induced emf in a coil perpendicular to a uniform magnetic field.
$\Phi _{B}\;=\;BA$	Magnetic flux.
$\epsilon \;=\;-N{\frac {d\Phi _{B}}{dt}}$	Induced emf in a coil.
$I\;=\;{\frac {Blv}{R}}$	Induced current from a conductor moving through a magnetic field.
$L\;=\;{\frac {N\Phi _{B}}{I}}$	Inductance of an N-turn coil.
$\epsilon _{L}\;=\;-L\left({\frac {\epsilon }{L}}l^{-{\frac {tR}{L}}}\right)$	Self-induced emf proportional to the time rate of change.
$f\;=\;{\frac {1}{2\pi {\sqrt {L{\mbox{C}}}}}}$	Frequency of oscillation in an LC circuit.