Rolling

Rolling is when an object has both rotational and linear kinetic energy. The formula for the total kinetic energy of an object due to rolling is given by:

By the law of conservation of energy, if we take the change in the expression above, that would be equal to the change in potential energy of the rolling object.

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Of course, some deformities and dissipations occur so this type of ideal situation where an object perfectly rolls(known as rolling without sliding) is impossible to come by. However, rolling objects can resist frictional forces and mechanical dissipations much better than purely sliding objects so it's much more effective to roll something than slide it.

One thing to keep in mind is that both terms for the total rolling kinetic energy is that the velocities(angular and linear) are both about the center of mass which is important to know because if they weren't, while it would still be possible to do calculations, you'd need to use the parallel axis theorem.

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Only(and only) if the object is rolling without slipping, you can use the relationship between angular and linear velocity, being: