What is rolling motion? Discuss the motion of a disc rolling without slipping on a level surface. Hence find the condition for rolling without slipping.

Rolling motion describes the motion of an object in which it moves with a constant angular velocity, translating along a plane while rotating around its axis. A typical example is a disc rolling without sliding on a level surface. For this case, the disc moves about its center, and a point of contact with the plane momentarily remains stationary, or doesn’t slide.

In rolling motion, there has to be some relationship between its linear velocity and angular velocity if the disc rolls without slipping. The linear velocity of the disc’s center of mass must, therefore, match the product of its angular velocity and radius for the disc to roll smoothly, without sliding at the point of contact.

Friction plays a very important role in this process. Static friction between the disc and the surface prevents slipping, allowing the disc to maintain its rolling motion. If the linear velocity exceeds this relationship, the disc will start to slip, breaking the condition of rolling without slipping.

In summary, rolling motion is characterized by the combination of translation and rotation. For a disc to roll without slipping on a level surface, the static friction must be sufficient to maintain the proper relationship between the disc’s linear and angular velocities.

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