Question

can angular displacement b both scalar and vector??

Answer 1

I would rather say it is a signed scalar:

Angular velocity is a vector because when you add two of them, they will add up as vectors.

But adding angular displacements truly as vectors implies having different axes of rotation, having angular origins for both axes. Well it's technically possible, but I've always seen velocities being added up, never displacements.

Answer 2

Finite angular displacements are not vector quantities, the reason being that they do not obey the law of vector addition. This law asserts that the order in which vectors are added does not affect their sum.
However finite angles under addition tend towards commutivity as the angles become very small. Infinitesimal angles do commute under addition, making it possible to treat them as vectors.

Answer 3

Only for very small angular displacements means infinitesimally small, we can consider then as vectors, not for any finite ang. dis., because in the later case they donot follow vector laws.

Answer 4

@kropot72's answer is correct if axes are independent of the body concerned.

If axis belong to the body, you can commute rotations, even non infinitesimal.

Answer 5

@Vincent-Lyon.Fr In the case of an axis belonging to a body would you consider angular displacements to be signed-scalars rather than vectors?

Answer 6

Yes, I would. I never saw angular displacements considered as vectors.