  The rotation of erupting filaments in the solar corona is addressed through a
parametric simulation study of unstable, rotating flux ropes in bipolar
force-free initial equilibrium. The Lorentz force due to the external shear
field component and the relaxation of tension in the twisted field are the
major contributors to the rotation in this model, while reconnection with the
ambient field is of minor importance. Both major mechanisms writhe the flux
rope axis, converting part of the initial twist helicity, and produce rotation
profiles which, to a large part, are very similar in a range of shear-twist
combinations. A difference lies in the tendency of twist-driven rotation to
saturate at lower heights than shear-driven rotation. For parameters
characteristic of the source regions of erupting filaments and coronal mass
ejections, the shear field is found to be the dominant origin of rotations in
the corona and to be required if the rotation reaches angles of order 90
degrees and higher; it dominates even if the twist exceeds the threshold of the
helical kink instability. The contributions by shear and twist to the total
rotation can be disentangled in the analysis of observations if the rotation
and rise profiles are simultaneously compared with model calculations. The
resulting twist estimate allows one to judge whether the helical kink
instability occurred. This is demonstrated for the erupting prominence in the
"Cartwheel CME" on 9 April 2008, which has shown a rotation of \approx 115
degrees up to a height of 1.5 R_sun above the photosphere. Out of a range of
initial equilibria which include strongly kink-unstable (twist Phi=5pi), weakly
kink-unstable (Phi=3.5pi), and kink-stable (Phi=2.5pi) configurations, only the
evolution of the weakly kink-unstable flux rope matches the observations in
their entirety.
