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1 Physics 1 Equations
2 Physics 2 Equations
- 2.1 Exam 1
- 2.2 Exam 2

[edit] 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

[edit] Physics 2 Equations

[edit] 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

[edit] 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.