Hoekmomentum: stijf lichaam

The angular momentum of a rigid body, made up of tiny particles and rotating about the z-axis with an angular velocity of ω, is the sum of the angular momenta of all such tiny particles.

A particle's angular momentum is equal to the cross product of its position vector and its linear momentum. By expressing the linear momentum in terms of linear velocity, which is tangential, the magnitude of the particle's angular momentum becomes m_iv_ir_i.

Now, expressing linear velocity in terms of angular velocity, an expression for the magnitude of total angular momentum is derived.

Here, the sum of m_ir_i² is equal to the moment of inertia I. Thus, the total angular momentum of the rigid body becomes Iω.

If the rigid body rotates about a symmetrical axis, its moment of inertia is constant, and hence, its angular momentum and angular velocity are parallel to the rotational axis.