User:JoshuaTree

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[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.
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