In uniform circular motion, angular velocity is defined as a vector quantity, regardless of whether the angular displacement is finite or infinitesimal. The confusion arises from the properties of vector addition, where finite angular displacements do not adhere to associative and commutative laws. However, infinitesimal angular displacements are considered true vectors. The discussion highlights the distinction between finite and infinitesimal angular displacements in relation to vector characteristics. Ultimately, angular velocity remains a vector quantity in both cases.
