Main Question or Discussion Point
Hey guys, we are currently studying chapter 10 in the Fundamentals of Physics 8th. Ed. Halliday & Resnick Textbook and I am having a little problem understanding the Parallel-Axis Theorem. I understand that the Moment of Inertia (Rotational Inertia) is derived from the Kinetic Energy Formula for Rotational Motion of a rigid body. However, the Parallel-Axis Theorem allows us to formulate the Moment of Inertia of a particular rigid body about an axis parallel to the axis of the center of mass. What I do not understand is why the formula for the Parallel-Axis Theorem has Icm + MD^2??? Why do you include the Icm and not just take the differential mass element at some distance "r" from the axis of rotation and calculate it that way - is this way more complicated? The way I interpreted the Icm part is that it represents the differential mass element of the rigid body right at some distance "r" from the new axis of rotation right? I totally understand the whole Moment of Inertia is I = integral r^2 dm which is the same thing as the MD^2 portion of the parallel-axis theorem right? I guess I am just trying to figure out why there is that plus in the middle of the formula and what it all means? Could someone please help clarify this for me because its just confusing to me. Thanks.