Torque direction meaning?

Question

I apologize if this question is dumb, but I've looked all over for a straightforward answer and either I can't find one or the terms are too complex for me to understand. I have only a rudimentary knowledge of Mechanics, but I do understand basic Linear Algebra. So torque, mathematically, is the cross product of the radial distance vector and a force vector. This cross product gives another vector that is orthogonal to both vectors and it points either outside or towards the "page" (in the context of a two dimensional diagram). Assuming this is correct, I do not understand what it pointing in or out means. Does it even have a phyisical, intuitive meaning? The best answer I've been able to come up with is that it's just a mathematical convention with no actual phyisical meaning, meant to provide a framework within which operations between torque vectors, such as addition and substraction, make sense. Am I correct or way off the mark here?

Answer 1

The interpretation of torque, and many other rotational vector quantities, is that these vectors all point in the direction of and along the axis of rotation. Moreover, the direction of these vectors is related to the direction of rotation using the so-called "right-hand rule". More specifically, for a torque that is pointing in the positive z-direction, the direction of rotation will be counterclockwise around the z-axis (looking from above the x-y plane). Alternatively, for a torque that is pointing in the negative z-direction, the direction of rotation will be clockwise around the z-axis.

This same convention applies to many rotational vector quantities, including angular velocity, angular acceleration, angular momentum, and even angular displacement.