A sphere is rolled across a rough horizontal surface. It gradually...

When a sphere rolls on a rough horizontal surface, it gradually decelerates due to rolling friction. The normal force from the surface shifts slightly forward in the direction of motion due to the deformation of the surface.

This shifted normal force creates a retarding torque opposite to the direction of rotation, which decreases the angular velocity $\omega$.

As $\omega$ decreases, the velocity of the bottommost point of the sphere tends to become forward relative to the ground, since $v > \omega R$.

To oppose this relative forward slipping, the force of static friction acts in the backward direction.

This backward frictional force opposes the linear motion, thereby attempting to decrease the linear velocity.

The torque produced by this frictional force about the center of mass acts in the direction of rotation, thereby attempting to increase the angular velocity.

Therefore, the force of friction attempts to decrease the linear velocity and increase the angular velocity.