Next we consider the physical pendulum (or compound pendulum) illustrated below.
Example 2
The pendulum is free to rotate about an axis through \( A \). The center of mass is denoted by \( C \) and \( \theta \) is the angle between \( A C \) and the vertical. Determine the equation of motion for the pendulum.
Solution
\[
M_{z}=I_{z} \ddot{\theta},
\]
for rotation about the \( z \)-axis. To write \( M_{z} \) in terms of \( m, g \) and \( \theta \) is Exercise 2.4.2 no. 2. (Its motion is described by the same differential equation - except for the parameters - as for the simple pendulum.)