In given figure, for pure rolling of spheres (a) Friction on...

In given figure, for pure rolling of spheres (a) Friction on $B$ hetwcen plank and spheres is in backward dircction (b) Friction on $A$ betwcen plank and spheres is in forward direction and $B$ in backward direction (c) Triction belwcen plank and spheres on hoth in forward dircction (d) Friction betwecn plank and spheres on both in backward direction

In given figure, for pure rolling of spheres
(a) Friction on $B$ hetwcen plank and spheres is in backward dircction
(b) Friction on $A$ betwcen plank and spheres is in forward direction and $B$ in backward direction
(c) Triction belwcen plank and spheres on hoth in forward dircction
(d) Friction betwecn plank and spheres on both in backward direction

Key Concepts

Pure Rolling

Pure rolling occurs when a rolling object's point of contact with the surface is momentarily at rest relative to the surface, which implies that there is no slipping between the surface and the rolling object. This condition is described by the relation v = ?R, where v is the translational speed, ? the angular speed, and R the radius. The concept is critical for understanding how rolling objects behave under the influence of friction and external forces.

Static Friction

In the case of pure rolling, the friction involved is static friction because the point of contact does not slide relative to the surface. Unlike kinetic friction, static friction adjusts its magnitude up to a maximum value to prevent slipping. It plays a crucial role in enabling rolling motion by providing the necessary force and torque balance that coordinates the translation and rotation of the object.

Direction of Friction Force

The direction of the static friction force on a rolling object is determined by the net external forces and the torque required for rotational motion. Friction may act in the forward or backward direction relative to the motion depending on whether it needs to accelerate or decelerate the center of mass and to produce a counteracting torque. Understanding the conditions under which friction acts helps in properly analyzing systems involving rolling motion on various surfaces.

Force and Torque Analysis in Rolling

Analyzing a rolling object requires considering both the translational motion (using Newton’s second law for forces) and the rotational motion (using Newton’s second law for torques). The friction force is pivotal in both analyses: it not only contributes to the net force on the object but also provides the torque about its center of mass. This dual role makes a detailed force and torque analysis essential for understanding the dynamics of any rolling motion.

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