The
angular momentum of an object rotating about an axis is defined as the
product of the moment of inertia (about that axis) with the angular
velocity. The
angular momentum of an object rotating about an axis is defined as the
product of the moment of inertia (about that axis) with the angular
velocity.
This satisfies the intuitive idea that moment of inertia is the "replacement" for mass in a rotational system. It also satisfies the more formal analogy for Newton's second law in linear and in rotational language: The net force is the time derivative of the linear momentum. The net torque should be the time derivative of the angular momentum.
Further comparison shows that the angular momentum for a particle can be defined without reference to moment of inertia, as the vector product of position and linear momentum. This can be extended to multiple particles, provided that the origin is the same for each position vector.
Perhaps the most interesting comparison is for the special case in which the net torque on a system is zero. In that case the angular momentum vector remains constant. In this situation, we say that angular momentum in conserved.
Conservation of angular momentum is as powerful an idea as conservation of linear momentum. It can have more spectacular consequences than linear momentum conservation, because of the peculiar nature of the moment of inertia. By changing the geometry of the rotating object, the moment of inertia changes. This change in the "replacement" for the mass produces a change in angular velocity, even though the angular momentum is constant.