In the given figure, for pure rolling of spheres: (a)...

In the given figure, for pure rolling of spheres:
(a) friction on $B$ is in forward direction
(b) friction on $A$ is in backward direction
(c) friction on $A$ and $B$ are in forward direction
(d) both (a) and (c) are correct

Key Concepts

Rolling Motion

Rolling motion involves both translational motion of the center of mass and rotational motion about the center. Analyzing rolling objects requires understanding how linear acceleration and angular acceleration are coupled, and how forces and torques act to produce this combined motion.

Rolling Without Slipping

Pure rolling, or rolling without slipping, is the condition where the point of contact between the rolling object and the surface is momentarily at rest relative to the surface. This relationship is characterized by the equation v = R?, linking the translational speed (v) of the center of mass to the angular speed (?) of the object through its radius (R).

Static Friction

Static friction is the frictional force that prevents relative motion between contacting surfaces when there is no slipping. In pure rolling, static friction not only stops slipping at the point of contact but also provides the necessary torque that either accelerates or decelerates the rotational motion without doing net work on the object.

Friction Direction in Rolling Dynamics

The direction in which static friction acts during rolling depends on the dynamic conditions of the motion. It may point in the same direction as the motion or opposite to it, depending on whether it is needed to increase or decrease the rotational speed relative to the translational speed, thereby ensuring the rolling without slipping condition is maintained.

Transcript

Please give Ace some feedback