Question

Consider the simplest rigid body, consisting of two point objects each of mass m, connected by a massless stick of length 2f. Suppose that the motion of this baton is to spin about an axis we'll choose to call , i.e. w = w2. We choose our origin at the center of mass, which is stationary. The angle between the AB axis and i is B.

Answer 1

$\omega\hat{z}=\omega(\cos\beta\hat{e}_1+\sin\beta\hat{e}_2)$

In $\hat{e}_k$ axis system the moment of inertia tensor is diagonal

$I_1=0,I_2=2ml^2, I_3=2ml^2$

Thus, the angular momentum is

$\vec{L}=I_1\omega_1\hat{e}_1+I_2\omega_2\hat{e}_2+I_3\omega_3\hat{e}_3$

$\vec{L}=2ml^2\omega\sin\beta\hat{e}_2$