# Why can any general motion of a rigid body be represented as translation + rotation about center of mass?

1. Why can any general motion of a rigid body be represented as translation + rotation about center of mass?

2. I am beginning to read rotational dynamics and my textbook states this fact without proof. I am wondering - Is this fact only true for a center of mass?

3. Then - The phrase "rotation about center of mass" strikes as vague to me. Rotation about which axis?

• You only need to prove that the rotation about CM, first about a certain axis with a certain angle, followed by another axis with another angle, is equivalent to a single rotation about a certain axis with a certain angle. Aug 1, 2016 at 21:21
• This fact is true not only about CM. The axis is to be determined by the actual configuration of the object. You can find the proof in e.g., Goldstein: Chasle's theorem --- the most general displacement of a rigid body is a translation plus a rotation. Aug 1, 2016 at 21:24