Many students have asked about when to include center of mass motion when calculating angular momentum and energy. In this page, we give a discussion of some of the main issues.
Issue 1: Pure Rotation and the Parallel Axis Theorem
Recognizing Pure Rotation
One key idea in determining how to describe rotational problems is recognizing whether the problem can be treated as pure rotation. Whenever an object is spinning around a fixed axle, we can choose to describe that motion as pure rotation about the axle, even if the center of mass is not located at the axle.
Two Descriptions of Pure Rotation: The Parallel Axis Theorem vs. Rotation and Translation
An object moving in pure rotation about an axle can be described in two different but equivalent ways.
- The object is only rotating, but the moment of inertia about the fixed axle must be found using the parallel axis theorem.
- The object is rotating about the center of mass and its center of mass is translating.
To see why these descriptions are equivalent, consider how we would find the angular momentum and energy of a bar pivoted at one end.