Angular Momentum of Objects in Linear Motion Practice Problems

Two identical space probes each with mass m are moving with equal but opposite momenta. The momentum of probe A is represented as $\vec{p}$ and that of probe B as $-\vec{p}$. The trajectories of the probes are not collinear. Is the total angular momentum of this system about any point in space constant, illustrating that it does not depend on the choice of origin?

In an engineering lab, a balancing wheel has two 40 cm rods, each with a 450 g mass at its end, mounted 180° apart on a central axle. The rods are spaced 60 cm apart along the axle, and the setup spins at 4.0 rad/s.

i. Calculate the axial component of the total angular momentum.

ii. Determine the angle between the angular momentum vector and the axle. [Hint: Compute the angular momentum vectors for both masses from a consistent reference point, possibly the center of mass.]