Energy

• Kinetic Energy

  • $E_k=\frac{1}{2}m{v}^2$ is the (translational) kinetic Energy
    • $m$ is the mass ($\mathsf{kg}$)
    • $v$ is the velocity ($m/s$)
  • $E_k=\frac{1}{2}I{\omega }^2$ is the rotational/angular kinetic energy
    • $I$ is the moment of inertia ($\mathsf{kg}\cdot {\mathsf{m}}^2$)
    • $\omega$ is the angular velocity ($rad/s$)

• Potential Energy

  • $E_p=mgh$ is the gravitational (potential) energy
    • $E_p$ is change in GPE ($\mathsf{J}$)
    • $m$ is the mass ($\mathsf{kg}$)
    • $g$ is the acceleration due to gravity ($m/{\mathsf{s}}^2$)
    • $h$ is the change in height ($\mathsf{m}$)
    • $\Delta \text{GPE}=m\cdot g\cdot \Delta h$
  • $E_p=\frac{1}{2}k{x}^2$ is the elastic (potential) energy
    • $E_p$ is the change in elastic potential energy ($\mathsf{J}$)
    • $k$ is the spring constant ($N/m$)
    • $x$ is the change in length ($\mathsf{m}$)
    • $\Delta \text{EPE}=\frac{1}{2}k\cdot \Delta x^2$
  • $U_E=k\frac{q_1{q}_2}{r}$ is the electric potential energy
    • $k$ is the Coulomb constant ($\mathsf{N}\cdot {\mathsf{m}}^2/{\mathsf{C}}^2$)
    • $q_1$ and $q_2$ are the charges ($\mathsf{C}$)
    • $r$ is the distance between the charges ($\mathsf{m}$)

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• Mechanical Energy
  • $E_{\text{total}}=E_k+E_p$
• $\Delta E=m\cdot c\cdot \Delta T$ is the change in thermal energy
  • $m$ is the mass ($\mathsf{kg}$)
  • $c$ is the specific heat capacity ($\mathsf{J}\cdot \mathsf{k}{\mathsf{g}}^{-1}\cdot {\mathsf{K}}^{-1}$)
  • $\Delta T$ is the change in temperature ($\mathsf{K}$)

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• todo
• $\frac{\text{electric potential energy}}{\text{charge}}=\text{electric potential}$
• $\text{voltage}=\text{(electrical) potential difference}=\Delta (\text{electric potential})$
• $\text{electric field}=$