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Momentum (conserved in collisions)

Linear	Rotational
Displacement $\overrightharpoon x$	Angle $\overrightharpoon \theta$
Mass $m$	Moment of inertia $I=\alpha MR^2$ where $M$ is mass and $R$ is the largest distance a particle is from axis or $I=\sum m_ir_i^2$ for $i$ th particle [ $kg\cdot m^2$ ]
Velocity $\overrightharpoon v={\overrightharpoon{\Delta x}\over\Delta t}$ [ $\frac{m}s$ ]	Angular velocity $\overrightharpoon \omega=\frac{\Delta\overrightharpoon \theta}{\Delta t}$ [ $\frac{\text{rad}}{s}$ ] $v_t=\|\overrightharpoon \omega\| r$ ([ $v_t$ =tangential velocity] must be in rads)
Momentum $\overrightharpoon p=m\overrightharpoon v$ [ $kg\cdot m\over s$ ]	Angular Momentum $\overrightharpoon L=I\overrightharpoon \omega$ [ $kg\cdot m^2\over s$ ]
Impulse $\overrightharpoon{\Delta p}=\overrightharpoon{p_f}-\overrightharpoon{p_0}$ [ditto] $\overrightharpoon{\Delta p}$ is also written as $J$	Twirl $\overrightharpoon{\Delta L}=\overrightharpoon{L_f}-\overrightharpoon{L_i}$ - change in angular momentum
Force $\overrightharpoon F=\frac{\overrightharpoon{\Delta p}}{\Delta t}$ - average impulse over time [ $N$ or $kg\cdot m\over s^2$ ]	Torque $\overrightharpoon \tau=\frac{\overrightharpoon{\Delta L}}{\Delta t}$ - average twirling over time [ $N\cdot m$ or $kg\cdot m^2\over s^2$ ]

$\Sigma E_i+W=\Sigma E_f$ - initial energy of system + work done on system = final energy of system
- energy [ $J$ ]
  - $K$ - kinetic energy (movement)
    - Translational: $K=\frac12m|\overrightharpoon v|^2$
    - Rotational: $K=\frac12I\omega^2$
  - $V$ - potential energy (interaction)
    - Gravitational: $V_G(r)=\frac{-Gm_1m_2}{r}$
      - where universal gravitational constant $\rm G=6.67\times10^{-11}\frac{N\cdot m^2}{kg^2}$
      - Simplification for on Earth: $V_G(z)=m|\overrightharpoon{g}|z$
        $z$ is height
        $|\overrightharpoon{g}|$ is $\rm 9.8 \frac{m}{s^2}$
    - Electrostatic: $V_e=\frac1{4\pi\epsilon_0}\frac{q_1q_2}r$
      - Coulomb’s constant $\frac1{4\pi\epsilon_0}=9\times10^9 \frac{\rm N~m^2}{\rm C^2}$
    - Spring: $V_s=\frac12kx^2$
      - $k$ is spring constant (specific to an individual spring)
        low value - easily moved
        high value - could not move (spring at end of train station)
      - $x$ displacement of spring
  - $U$ - internal energy (usually does not change that much)
    - nuclear energy
    - chemical energy
    - thermal energy
- work
  - $W=\overrightharpoon{F} \cdot \overrightharpoon{d}$
  - Watt (W) is $kg\cdot m^2\over s^3$ or $\frac{J}s$
  - Work is zero if there is no displacement/movement
- power (derivative of work)
  - $P=\frac{\Delta E}{\Delta t}=\frac{W}{\Delta t}=F\cdot v$
  - watt (W)=J/s
  - horsepower (hp)=746 W
- Forces
  - $|\vec{F}_{SF}|\leq\mu_{s}|\vec{F}_N|\approx|\vec{F}_{\text{SF,max}}|$
    - Static friction
    - $\mu_s$ depends on materials in contact
  - $|\vec{F}_{KF}|\approx\mu_{k}|\vec{F}_n|$
    - Kinetic friction
  - $|\vec{F}_D|\approx\frac12C\rho A|\vec v|^2$
    - Drag
  - ${F}_{sp}=-kx$
    - Spring force (AKA Hooke’s law)