Write an expression for the kinetic energy of a body rolling without slipping.

The kinetic energy of a rolling body is a combination of translational and rotational. An object that rolls has a linear velocity at its center of mass, as well as rotation about that center. Translational kinetic energy depends on the mass of the object and its velocity. This energy is associated with the motion of the entire body through space.

In addition to translational kinetic energy, the object has rotational kinetic energy because it is rotating about its axis. The amount of rotational energy depends on the moment of inertia of the object, which is a function of the mass distribution and shape of the object and its angular velocity, which is a measure of how fast it is rotating.
When an object rolls without slipping, there is a relationship between its linear velocity and angular velocity. Specifically, the center of mass velocity is directly proportional to the angular velocity of the object. This relationship forms the basis of the understanding for the conservation of energy in rolling motion. Consequently, the total kinetic energy of a rolling body is the sum of its translational and rotational energies, reflecting the movement through space and the rotation about its axis. This total energy is vital in the analysis of the dynamics of rolling objects within different physical settings.

Checkout for more contents: – https://www.tiwariacademy.com/ncert-solutions/class-11/physics/chapter-6/