Convention or reality?

Question

In case of a disc rotating about an axis perpendicular to its plane passing through its centre of mass, the torque vector points up or down depending upon direction of rotation. Is it just convention, or a physical force really acts parallel to the axis of rotation? In other words, if I spin the disc fast enough so that it’s torque points upwards in an environment with no air resistance, will it oppose gravity and stay in air?

Answer 1

The direction of torque (which, incidentally, is not really a vector but a pseudovector) is a matter of convention. It originates from the fact that we use the right-hand rule to define the direction of the vector cross product. If we used a "left-hand rule" instead then all torques would point in the opposite direction.

Answer 2

Direction of torque does not depend on Direction of rotation. A body can be rotating without any torque on it .Earth is rotating on its axis without any torque due to sun ( here r x F is zero) If angular velocity is changing then only torque is acting. For fixed axis of rotation if angular speed is increasing then torque and angular velocity are in same direction. If decreasing then in opposite direction. Torque can balance torque and force can balance force.

Answer 3

Looking down on a disk that is spinning clockwise, I report that the disk is spinning clockwise. However, if I look at the same disk from below, I report that the disk is spinning counter-clockwise. Thus, observers from either side of the disk can never agree. Due to that, the right hand rule was implemented such that a pseudo-vector (see reply from Gandalf61) is defined in a way that uniquely specifies a direction. Using the right hand rule, I look at the same spinning disk from above it and note that the angular momentum vector is pointing down. When looking at the same disk from below and using the right hand rule, I still note that the angular momentum vector is pointing down.