I was solving an exercise the other day, about a rolling cylinder on an inclined plane. Initially the cylinder slides, but then it begins to roll and the problem wanted to know the velocity of the Center of Mass at the instant in which the rolling motion begun. I instinctively applied $I_c \underline{\omega} = \underline{M_c}$ (all the moments expressed with respect to the Center of Mass) and solved the problem correctly according to the solution. However, after having given it some thought I realized that what I did was wrong: in fact, you can only apply such equation with respect to a point of instantaneous rotation (that is, a point instantaneously in quiet) or, in extreme cases, with respect to the Center of Mass when the istantaneous point of rotation exists and is at a fixed distance from the center and moving with it (which is not my case, since the point of istantaneous rotation moved from its initial position to the point of contact with the plane).
I would really like to know if I am right or wrong and why.
As always, any comment or answer is highly appreciated!
