Identify a fixed point of rotation for the object. This can be visualized as the rotational axis of a spinning circular top. Inertia is defined as the product of the mass times the distance squared from a single point of origin or central point (I = m*r^2). The point of rotation, therefore, will be used to identify the distance r of the object from the center . Using the spinning circular top example, r would be the radius of the top from its rotational axis. For a spinning figure skater, r would be the measure of the extension of the arms or a leg from the body.
Determine the object's mass. The inertia is directly proportional to the mass of the rotating object as well as the square of its distance from the rotational axis as previously discussed. By identifying the mass in addition to the distance r from the rotational axis, you now have the ability to describe a rotating object's inertia (I = m* r^2).
Identify the angular velocity. You have now described the inertia of a rotational object and need to identify the angular velocity. Angular velocity (w) is the velocity (v) multiplied by the angle between the velocity and momentum vector and is expressed as w = v*sin ?.
Multiply these two variables to derive the expression for angular momentum, which is the product of the inertia of an object and its rotational speed, or L = I*v. Angular momentum is a conserved property; therefore, the inertia of the rotating object is indirectly proportional to the angular velocity. As the mass or distance from the rotation axis increases (inertia), the velocity will decrease. Similarly, a decrease in the mass or distance decreases the inertia resulting in a subsequent increase in velocity. You can visualize this relationship with the spinning figure skater. As he extends his arms out, he is increasing the distance (r) from the rotational axis, which is his body. This results in a subsequent increase in the skater's inertia, which slows the body's rotational speed. Bringing his arms in closer to his body will decrease the resistance to the rotation or the inertia of his body and subsequently increase his speed.