A sphere is rolled across a rough horizontal surface. It gradually decelerates and comes to rest. The force of friction attempts to

Step-by-step solution

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 . As decreases, the velocity of the bottommost point of the sphere tends to become forward relative to the ground, since v > R . To oppose this relative forward slipp