List of Kinetic and Potential Energy
Contents
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 :
$$
\begin{align}
U = \frac{1}{2}kr^2
\end{align}
$$