Can you build a molecule where you can perform a rotation about double bond? Why?

Answer 1

The double bond has both a "sigma" (overlap) bond and a "pi" (donut shape) bond. It is very difficult to twist the pi bond and rotate the molecule.

This leads to the creation of geometric isomers, called cis and trans versions of the same molecular formula. They are isomers because they are not on the same side of the double bond, and the molecule cannot be twisted around.

Answer 2

Sure.
It's called 11-cis retinal and is a light sensitive pigment. It'll switch to its trans form in the presence of light -- which is a rotation about the double bond.