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It comes down to the way the bond forms. If we look at the double bond in carbon atoms, there is a pi bond forming above and below the plane of the carbon atoms. The bond, which is enabling the sharing of an electron, breaking would imply the p-orbitals not overlapping and allowing the sharing. Since things like to be in their lowest energy, it is easier to just not break the bond, hence there is an energy output required to break the pi bond.
It's based on the structure of the bonds. When we look at how the pi bonds are connected, there is no room for rotation without the bonds disconnecting. But when we look at sigma bonds, their cylindrical interaction allows rotation.
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