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Sigma bonds can be rotated because they interact end to end with one electron bonded end to end. Because this electron is bonded end to end makes it possible for the sigma bond to rotate without breaking. On the other hand, pi bonds interact side to side with one electron bonded side to side, making it very easy to break the bond if trying to rotate. In a pi bond, both end of the bond are bonded, leaving no room for rotation without breaking.
Additionally, sigma bonds have cyclical symmetry around the internuclear axis which allows the bound atoms to rotate. However, pi bongs have electron density on either side of the internuclear axis which prevents the bound atoms from rotating.
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