My book says
Because it (the sigma bond) lies along the line joining the two carbon atoms, the sigma bond can rotate about this axis.
But that doesn't make sense to me. So what if the sigma bond lies along the bond axis? How does that matter?
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2$\begingroup$ The sigma bond has symmetry akin to that of a cylinder. The energy is the same no matter what the rotation angle, thus rotation is possible. The energy does, however, depend greatly on separation of atoms as the balance of charges (protons/electrons) is upset. In a pi bond the symmetry is different and energy is needed to remove the p to p electron overlap on the two atoms, so free rotation is not possible. $\endgroup$ – porphyrin Feb 14 '17 at 17:48
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Sigma bonds are defined as having their electron density along the bond axis, while pi bonds have their electron density above and below the bond axis. What this mean is that pi bonds cannot rotate the same way as sigma bonds since rotation would break the pi bond interaction. See the picture below for clarification.
If you're wondering why it rotates then the more freely that a bond rotates, the more favorable the entropy. In general, the more kinds of motions and the more unconstrained those motions are, the more favorable the entropy.
