The expressions of work in pure translation in x- direction (one dimensional linear motion) is given by :

The corresponding expressions of work in pure rotation (one dimensional rotational motion) is given by :

Obviously, torque replaces component of force in the direction of displacement (Fx) and angular displacement (θ) replaces linear displacement (x). Similarly, the expression of kinetic energy as derived earlier in the course is :

Here, moment of inertia (I) replaces linear inertia (m) and angular speed (ω) replaces linear speed (v). We, however, do not generally define gravitational potential energy for rotation as there is no overall change in the position (elevation) of the COM of the body in pure rotation. This is particularly the case when axis of rotation passes through COM.

This understanding of correspondence of expressions helps us to remember expressions of rotational motion, but it does not provide the insight into the angular quantities used to describe pure rotation. For example, we can not understand how torque accomplishes work on a rigid body, which does not have any linear displacement ! For this reason, we shall develop expressions of work by considering rotation of a particle or particle like object in the next section.

We need to emphasize here another important underlying concept. The description of motion in pure translation for a single particle and a rigid body differ in one very important aspect. Recall that the motion of a rigid body, in translation, is described by assigning motional quantities to the "center of mass(COM)". If we look at the expression of center of mass in x-direction, then we realize that the concept of COM is actually designed to incorporate distribution of mass in the body.

We must note here that such distinction arising due to distribution of mass between a particle and rigid body does not exist for pure rotation. It is so because the effect of the distribution of mass is incorporated in the definition of moment of inertia itself :

For this reason, there is no corresponding "center of rotational inertia" or "center of moment of inertia" for rigid body in rotation. This is one aspect in which there is no correspondence between two motion types. It follows, then, that the expressions of various quantities of a particle or a rigid body in rotation about a fixed axis should be same. Same expressions would, therefore, determine work and kinetic energy of a particle or a rigid body. The difference in two cases will solely arise from the differences in the values of moments of inertia.