The centre of gravity of any cylinder is the point of bisection of the axis.
For a physicist or a mathematician, the most symmetrical object you could think about would be a sphere, because it looks identical no matter what you do to it, however you rotate it in any given direction.
You can widen the feet of a compass, but they are still attached at the top; you can spin them away from each other, but you always wind up where you started.
Symmetry principles are principles governing the laws of nature that say those laws look the same if you change your point of view in certain ways.
Symmetry does mean something different for physicists than for members of the public. It means that an object or a theory does not change when you make some transformation - either rotating or moving it or doing something to the equations.
An object is chiral if it cannot be brought into congruence with its mirror image by translation and rotation.
The law of right-left symmetry was used in classical physics but was not of any great practical importance there. One reason for this derives from the fact that right-left symmetry is a discrete symmetry, unlike rotational symmetry, which is continuous.
To grasp the essence of chirality, it is instructive to withdraw for a moment from the familiar three-dimensional world into a two-dimensional one, into a plane, and enquire what chirality means there.
