User:JoshuaTree

Physics 1 Equations

$v_{xf}=v_{xi}+a_{x}t$	Velocity as a function of time
$x_f=x_i+\frac{1}{2}(v_{xi}+v_{xf})t$	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
$v_{xf}^2=v_{xi}^2+2a_x(x_f-x_i)$	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
$W\equiv F\mathrm{\Delta }r\cos \theta$	The amount of work done on a system
$K\equiv \frac{1}{2}m{v}^2$	Kinetic energy of a particle
$U_g\equiv mgy$	Gravitational potential energy
$U_s\equiv \frac{1}{2}k{x}^2$	Elastic potential energy
$K_f+U_f=K_i+U_i=\frac{1}{2}m{v}_f^2+mg{y}_f=\frac{1}{2}m{v}_i^2+mg{y}_i$	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
$a=\frac{q\text{E}}{m}$	Acceleration of a particle in a uniform electric field
${\mathrm{\Phi }}_{\text{E}}=\text{E}A\cos \theta$	Electric flux through a surface of fixed area
${\mathrm{\Phi }}_{\text{E}}=4\pi k_{e}q$	Electric flux through a gaussian sphere
${\mathrm{\Phi }}_{\text{E}}=\frac{q_{in}}{{ϵ}_0}$	Gauss's Law
$\text{E}=k_e\frac{Q}{r^2}$	Electric field at a point outside an insulating solid sphere with uniform charge density
$\text{E}=k_e\frac{Q}{a^3}r$	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
$\text{E}=\frac{\sigma }{{ϵ}_0}$	Electric field from surface charge density
$\mathrm{\Delta }U=q_0\mathrm{\Delta }V$	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
$\text{C}\equiv \frac{Q}{\mathrm{\Delta }V}$	Capacitance
$\mathrm{\Delta }V=\text{E}d=\frac{Qd}{{ϵ}_{0}A}$	Potential between parallel plates
${\text{C}}_{eq}={\text{C}}_1+{\text{C}}_2+...$	Capacitors in parallel
$\frac{1}{{\text{C}}_{eq}}=\frac{1}{{\text{C}}_1}+\frac{1}{{\text{C}}_2}+...$	Capacitors in series
$R=\rho \frac{l}{A}$	Resistance of a uniform material along length
$R\equiv \frac{\mathrm{\Delta }V}{I}$	Resistance as a ratio of potential difference to the current
$I=\frac{ϵ}{R+r}$	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
${𝒫}=I\mathrm{\Delta }V$	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
$K=\frac{1}{2}m{v}^2=\frac{q^2{B}^2{R}^2}{2m}$	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.
$\left|ϵ\right|=N\frac{\mathrm{\Delta }\left(BA\right)}{\mathrm{\Delta }t}$	Induced emf in a coil perpendicular to a uniform magnetic field.
${\mathrm{\Phi }}_B=BA$	Magnetic flux.
$ϵ=-N\frac{d{\mathrm{\Phi }}_B}{dt}$	Induced emf in a coil.
$I=\frac{Blv}{R}$	Induced current from a conductor moving through a magnetic field.
$L=\frac{N{\mathrm{\Phi }}_B}{I}$	Inductance of an N-turn coil.
${ϵ}_L=-L\left(\frac{ϵ}{L}{l}^{-\frac{tR}{L}}\right)$	Self-induced emf proportional to the time rate of change.
$f=\frac{1}{2\pi \sqrt{L\text{C}}}$	Frequency of oscillation in an LC circuit.
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