Angular momentum characterizes an object's rotational motion and is defined as the moment of its linear momentum about a specified point O. When a particle moves along a curved path in the x-y plane, the scalar formulation calculates the magnitude of its angular momentum, utilizing the moment arm (d), representing the perpendicular distance from point O to the line of action of the linear momentum. Despite being scalar in formulation, angular momentum is inherently a vector quantity. Its direction is ascertained through the right-hand rule, perpendicular to the rotation plane.

If the particle traces a space curve, the vector cross-product becomes instrumental in determining the angular momentum around a specific point. In this representation, the angular momentum maintains orthogonality to the plane formed by the position vector and linear momentum. For computations involving the cross product, expressing the position vector and linear momentum in Cartesian components is crucial. The angular momentum is then established by evaluating the determinant formed by these components. This comprehensive approach ensures an accurate representation of angular momentum in both magnitude and direction for objects undergoing rotational motion.