I understand that the center of mass is a point which can be considered to contain all of an object's mass, for the purpose of calculations involving universal gravitation. I also understand that the center of mass of an object of uniform density is located at the centroid. In this case, I understand that the center of mass follows a path identical to that of a point mass subjected to the same initial forces, and that any rotation is around the centroid/COM. This makes sense to me because of the conservation of linear momentum (the net momentum due to rotation is zero, so the object behaves as a point mass). However, an object with non-uniform density necessarily has a center of mass outside it's geometric center. In this case, if the object is subjected to a force and a torque, if the object is to maintain rotation at constant angular velocity around it's COM, momentum due to rotation cannot equal zero (the less dense parts of the object are located farther from the center of mass and thus have greater linear velocity). How can an object of non-uniform density maintain rotation at constant angular velocity around its center of mass if the direction of momentum due to rotation is constantly changing? It seems that the object would be pulled in different directions due to "uneven" linear momentum. Please correct my flawed reasoning if possible.