Discuss whether or not , angular displacement is a vector quantity ?`

Explanation

Angular displacment represent rotational effect, So, appers to be an axial vector. Furthermore as it obeys the law of parallelogram of addition so it may be a vector. However, it has been fround that large angular displacement does not obey the law of commutation while infinitestimal do, i.e.,
`vectheta_(1) + vectheta_(2) ne vectheta_(2) + vectheta_(1) `but `dvectheta_(1)+ dvectheta_(2)= dvectheta_(2)+ dvectheta_(1)`
This is self-evident from Fig.3.19. So, angular displacement is a vector if small and not a vector if large.

Note: (i) From this exmaple it is clear that certain physical quantities can behave either as a scalar or a vector and how the circumstance. THis is somewhat like dual nature of light or matter.
(ii) Here it is also worthy to note that there are also certain phycsical quantites which behave neither as scalar nor as Vector. For example , moment of inertia is not a vector. For example, moment of inertia is not a vector as by changing the sense of rotation its value is not changed . It is also not a scalar as it has different