What is physical significance of the direction of angular velocity?

[mdcreator]

This question has been bugging me for quite a while, That what do we mean by direction of angular velocity or torque. As we know that the direction of angular velocity or torque even is determined by right hand thumb rule, and it come out to be perpendicular to the rotational plane. So my question is what does this direction signify? Specifically what does it signify physically?

 

[A.T.]

... it come out to be perpendicular to the rotational plane. So my question is what does this direction signify?

You have just answered your own question: It describes the orientation of the rotational plane (as its normal) or of the rotational axis (as its parallel).

However, this still gives you two possible vector orientations which represent two rotation directions in that plane. The correspondence here is an arbitrary convention, and has no physical reason. We could have just as well agreed to using the left hand rule.

 

[Lnewqban]

Welcome, @mdcreator !

At first glance, the convention may seem to be useless for rotational velocity and torque of a disc, but it helps when things get more complicated.

Examples:
In cases where applied moment induces a opposite rotational acceleration that is retarding the angular velocity.

Estimating the combined direction of angular velocity or torque of the above rotating disc which begins to simultaneously rotate about another axis and at a different rate.

Estimating the combined direction of changes of angular acceleration and angular momentum.

Please, see:
https://courses.lumenlearning.com/suny-osuniversityphysics/chapter/10-1-rotational-variables/