---
title: Notes on Physics
tags:
  - Physics
id: "3243"
categories:
  - - Life
    - Study
date: 2018-06-30 13:15:27
---

## 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

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