3. The slender rod AB is attached by a clevis joint to the arm BCD which rotates with
a constant angular velocity $\vec{\omega}$ as shown in Figure 3A. The moments of intertia for
a slender rod are $I_x \approx 0$, $I_y = I_z = \frac{1}{12}mL^2$ where x', y' and z' are the principal
axes and x' runs along the long axis of the rod.
a) If the center of mass of the rod AB lies halfway along the rod, then find its
angular momentum $\vec{H}_G$, about the center of mass in terms of m, L and $\omega$.
[4 marks]
b) Find the time rate of change of angular momentum about the center of
mass $\dot{\vec{H}}_G$, in terms of m, L and $\omega$. [4 marks]
c) Find the value of angular velocity $\omega$ that maintains the slender rod AB in
this position (i.e. at 30° with respect to horizontal). [6 marks]
Hint: $\dot{\vec{H}}_G = \sum \vec{M}_G$
Figure 3A
