Discuss why an infinitesimal displacement is regarded as a vector quantity.
Infinitesimal rotations may be regarded as vector quantity because they are described by the body in a small interval of time is more or less a straight line and is thus representable as a vector.
Note: In some of the books it is written that large angular displacement does not obey the law of
commutation (→θ1+→θ2≠→θ2+→θ1)
So, they cannot be treated as vectors while infinitesimal do. So, they are vectors. As per my opinion the sufficient and necessary condition to be a vector is that is should obey the law of parallelogram of vector. If this is satisfied the law of commutation is automatically satisfied. It can be explained and proved in a better way but that require three dimensional treatment. Which I feel is not necessary for any competition.
Infinitesimal rotations may be regarded as vector quantity because they are described by the body in a small interval of time is more or less a straight line and is thus representable as a vector.
Note: In some of the books it is written that large angular displacement does not obey the law of
commutation (→θ1+→θ2≠→θ2+→θ1)
So, they cannot be treated as vectors while infinitesimal do. So, they are vectors. As per my opinion the sufficient and necessary condition to be a vector is that is should obey the law of parallelogram of vector. If this is satisfied the law of commutation is automatically satisfied. It can be explained and proved in a better way but that require three dimensional treatment. Which I feel is not necessary for any competition.
