A solid homogenous sphere of mass M and radius R is moving on rough horizontal surface, partly rolling and partly sliding. During this kind of motion of this sphere

A solid homogeneous sphere of mass and radius is moving on a rough horizontal surface. In this case, the sphere rolls and slides. The dynamics of the sphere are complex because of the interaction between translational and rotational motions. When the sphere moves, it experiences friction from the surface, which affects its motion. Frictional force at the point of contact between the sphere and the surface exerts a torque on the sphere, which is a factor changing the angular momentum of the sphere.

Total kinetic energy is not conserved during this type of motion because part of the energy is converted to heat due to friction. The angular momentum of the sphere about the point of contact with the surface can be conserved. This conservation takes place under certain conditions where no external torques act on the sphere about that particular point. Thus, even as the sphere rolls and slides, the angular momentum can be analyzed effectively using the point of contact as a reference. This situation highlights the interplay between different types of motion and the principles governing angular momentum in systems with friction. This is important to understand in the study of physics and engineering because one needs to know how objects move under various forces.

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