15.11 :  運動方程式: 固定軸を中心とした回転

Imagine a flywheel having a non-uniform mass, rotating around a fixed axis. As the flywheel spins, its center of mass moves in a circular path.

The acceleration of the center of mass is described by its tangential and normal components.

The tangential component of acceleration depends on the direction of the angular acceleration of the flywheel. In contrast, the normal component of acceleration is always along the radius and towards the point O.

The moment exerted on the flywheel's center of mass is determined by the product of its moment of inertia of the center of mass and its angular acceleration.

The moment equation can be written in terms of the moment about point O to eliminate any unknown force acting on the body.

Here, the moment due to the normal component of the acceleration is not considered as it passes through point O.

Using the parallel axis theorem, the moment equation can be expressed in terms of the moment of inertia about point O.