| − | Suppose a rod of mass m and length L is rotating about one end. As the rod is continuous, we use the integration form. Therefore in terms of differentials, dI=r<sup>2</sup>dm. Defining the [[density]] of the rod as λ=m/L, dI can be written as dI=r<sup>2</sup>λdr. Integrating gives moment of inertia: | + | Suppose a rod of mass m and length L is rotating about one end. As the rod is continuous, we use the integration form. Therefore, in terms of differentials, dI=r<sup>2</sup>dm. Defining the [[density]] of the rod as λ=m/L, dI can be written as dI=r<sup>2</sup>λdr. Integrating gives moment of inertia: |