Notes on Physics

One-dimensional motion

$$
\begin{align}
v_f&=v_i+a \Delta t \\
\Delta x&=v_i \Delta t+{a \Delta t^2 \over 2} \\
\Delta x&={v_i+v_f \over 2} \Delta t \\
v_f^2&=v_i^2+2a \Delta x
\end{align}
$$

Forces and Newton’s laws of motion

$$
\begin{align}
F=ma
\end{align}
$$

Centripetal force and gravitation

$$
\begin{align}
a&={v^2 \over r}=\omega^2r \\
F&=G{m_1m_2 \over r^2}
\end{align}
$$

Work and energy

$$
\begin{align}
K&={mv^2 \over 2} \\
U_g&=F_gh=mgh \\
P&={W \over t}={Fx \over t}=Fv=mav
\end{align}
$$

Electric charge, field, and potential

$$
\begin{align}
F&=k{Q_1Q_2 \over r^2} \\
E&=k{Q \over r^2} \\
E&=2 \pi k \sigma \\
U_e&=k{Q_1Q_2 \over r} \\
V&=k{Q \over r}
\end{align}
$$

Circuits

$$
\begin{align}
R&={V \over I} \\
C&={Q \over V} \\
C&={A \over 4 \pi kd} \\
P&={U \over t}={U \over Q} \cdot {Q \over t}=VI=I^2R \\
W&=Pt=VIt=I^2Rt
\end{align}
$$

Magnetic forces, magnetic fields, and Faraday’s law

$$
\begin{align}
F&=QvB={Q \over t}(vt)B=ILB={B^2L^2v \over R} \\
B&={\mu_0I \over 2 \pi r} \\
\Phi&=BA \\
E&=N{\Delta \Phi \over \Delta t}=N{B\Delta A \over \Delta t}=NBLv \\
V_s&=V_p{N_s \over N_p}
\end{align}
$$

Momentum

$$
\begin{align}
I=mv=QLB={B^2L^2x \over R}
\end{align}
$$