Final answer:
The angular momentum vector of a spinning flywheel is determined by the right-hand rule and points along the axis of rotation. It remains constant over time if no external torques act on the system, as per the law of conservation of angular momentum.
Step-by-step explanation:
If the change in angular momentum (L) is zero, then the angular momentum is constant; this occurs when the net torque (T) is equal to zero. Angular momentum is then conserved, as stated by the law of conservation of angular momentum, which can be particularly relevant in the absence of external torques or in collisions.
The angular momentum is given by the vector product of the position vector r and the linear momentum p of the particle (l⃗ = r × p). For an object like a flywheel that is spinning about its axis, the angular momentum vector can be determined using the right-hand rule, where the vector points in the direction of the spinning axis. If the system exhibits no time dependence in the expression for angular momentum and no external torque acts on it, the angular momentum remains constant over time.
In the case of a symmetrical rotating body such as a flywheel, the perpendicular components of angular momentum cancel out due to cylindrical symmetry, and only the axial component contributes to the net angular momentum. Therefore, at t = 0, the angular momentum vector about the pivot will point along the axis of rotation, in the direction given by the right-hand rule, with a magnitude determined by the product of the rotational inertia and angular velocity of the flywheel.