Final answer:
The net torque is perpendicular to both the radius from the pivot to the wheel's center and the wheel's spin axis. The spin angular momentum points from point B to A if the wheel spins counterclockwise. The wheel precesses clockwise from the view above the pivot, and the determination of the moment of inertia requires additional information.
Step-by-step explanation:
The question you've asked involves concepts from classical mechanics, specifically rotation and angular momentum. To address the issues given, one needs to apply the principles of torque, angular velocity, and moment of inertia, which are all fundamental concepts in physics.
a. The direction of the net torque on the wheel about the pivot point P is perpendicular to both the radius from P to the center of mass of the wheel and to the spin axis because the weight of the wheel creates a torque due to gravity at the center of mass of the wheel, which is not aligned along P.
b. If the wheel is spinning counterclockwise as seen from point B, the direction of its spin angular momentum is along the axle, pointing from point B to point A, following the right-hand rule for angular momentum.
c. As seen from point A above the pivot, the wheel is precessing clockwise. This is deduced from the right-hand grip rule: if the fingers of the right-hand point in the direction of the wheel's spin, the thumb will point in the direction of the precession.
d. To determine the moment of inertia I of the wheel about its axle, we use the conservation of angular momentum and the given parameters such as mass distribution and rotational rates. However, to calculate it specifically, we would need additional information such as the geometry of the wheel and the axle assembly.