# "One can properly speak of the angular velocity of a rotating object without reference to a specific axis of rotation"?

In A.P. French's Newtonian Mechanics, page $$662$$, one can read,

The kinetic energy of a system is equal to the kinetic energy associated with the linear velocity of the center of mass, $$C$$, plus the energy of rotation about the center of mass:$$K=\frac{1}{2}Mv_{c}^{2}+\frac{1}{2}I_{c}\bigg ( \frac{d\theta}{dt}\bigg )^{2}$$ The term representing the rotational energy about the center of mass in this equation embodies an important feature. If the object has angular velocity $$d\theta /dt$$ about its true axis of rotation through $$O$$, every point in it is also has the angular velocity $$d\theta /dt$$ about a parallel axis through $$C$$, or through any point for that matter. One can properly speak of the angular velocity of a rotating object without reference to a specific axis of rotation. Any line drawn on a rotating disk, for example, has the same rate of angular displacement as one of the radii.

What does the author mean when he says even if an object is not rotating about an axis, it nevertheless has an angular velocity about that axis similar to the one about the true axis of rotation? Aren't these two assertions in contradiction with each other?

• Picture a composite object that is composed of two "sub" objects, that are rigidly connected to each other. Now suppose that the whole composite is rotating about its center of mass. Sounds like the author could be talking about the individual contribution of either of the sub-objects, each of which is rotating, but rotating about an axis that does not pass throug its own center of mass... Maybe? Commented Feb 13, 2020 at 21:41

## 1 Answer

[https://i.sstatic.net/SSetZ.png">Hello look at the picture, the disk is rotating, a radius has angular velocity w, the other rod in the picture has the same angular velocity as the radius moving fron the black position to the red one.