hexo-blog/source/_posts/life/notes-on-physics.md

---

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

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