List of Kinetic and Potential Energy

List of Kinetic and Potential Energy#

For a set of arbitrary positional parameters,

\[r = r(x, y, z, ...)\]

May be transformed into any other coordinate…

Kinetic Energy#

General Definition : $\( \begin{align} K_\text{lin} &= \frac{1}{2}m\dot r^2\\ K_\text{rot}&=\frac{1}{2}I\dot\phi^2\\ \end{align} \)$

  • \(I\) : Moment of inertia where, \(I=\int{Mr\;dR}\)

Potential Energy#

Gravity : $\( \begin{align} U_g &= -\frac{GMm}{r} &\\ U_g &= -mgh \end{align} \)$

\(g\) : Gravitational acceleration which, \(g=\frac{GM}{R^2}\) for a constant \(M\) and \(R\).

Hooke’s Law :

$$
\begin{align}
    U = \frac{1}{2}kr^2
\end{align}
$$
Contents