Wheel rolling: If the pulley itself rotates by rolling in motion and has its own moment of inertia and angular velocity, the rotational kinetic energy of the pulley should be considered.
The pulley has mass: if the pulley has a certain mass, its movement will have a combination of translation and rotation, so it is necessary to consider the centroid movement and rotation movement of the pulley, which involves the kinetic energy of the pulley.
In the above case, the kinetic energy of the pulley is a part of the total kinetic energy of the motion system, which is usually considered in energy conservation or dynamic analysis. It is necessary to determine whether to consider the kinetic energy of pulleys according to specific physical problems and motion scenes. In some simplified cases, the pulley can be regarded as a particle or its kinetic energy can be ignored, but in the problems involving its own motion characteristics, the kinetic energy of the pulley needs to be considered.