What is the difference and connection between the angular momentum theorem and the rotation law of a rigid body rotating on a fixed axis?

The relationship between the theorem of angular momentum and the law of rotation: the angular momentum of a rigid body rotating around a fixed axis is equal to the product of the moment of inertia of the rigid body and the angular velocity; The direction is the same as the angular velocity.

The difference between angular momentum theorem and rotation law;

First, the content is different.

1, angular momentum theorem:? The derivative of angular momentum of a particle system to a point (or axis) with respect to time is equal to the principal moment of the external force system to the point (or axis).

2. Law of rotation: refers to that the resultant moment of a rigid body on a fixed axis is equal to the product of the inertia moment of the rigid body on a fixed axis and the angular acceleration of the rigid body under the action of this resultant moment.

Second, the use is different.

1, angular momentum theorem: widely used to deal with the rotation of a rigid body at a fixed point (or axis).

2. Rotation law: used to calculate the angular velocity and angular acceleration of a rigid body rotating around a fixed axis.

Third, the formula is different.

1, angular momentum theorem: the differential form of angular momentum theorem is dl/dt = m.

2. Law of rotation: Mz=Jβ, where Mz represents the resultant torque of a certain axis, J represents the moment of inertia of a rigid body around a given axis, and β represents angular acceleration.

Baidu encyclopedia-angular momentum theorem

Baidu encyclopedia-law of rotation