But the Sun is supposed to turn into a Red Giant as it burns up its hydrogen. Such stars are not very dense in their outer layers. I dunno how the rotation would be affected.
But it's not a pretty future. http://en.wikipedia....un_as_a_red_giant
More on "tidal locking" here - http://en.wikipedia....iki/Tidal_locking
HTH.
Cheers,
Scott.