Physical Origin of Pseudovector Exemplified by Torque

Abstract

In college physics, cross product and pseudovector are always very confusing for most students. Here we explain from the bottom why cross product is defined as the mysterious determinant appeared in every textbook. Only middle-school knowledge of lever principle is required in the derivation. Furthermore, we introduce a strict definition of physical vector according to the transformation property under space rotation, and show explicitly that cross product of two real vectors is still a vector. Such vector is a pseudovector due to its special transformation property under space inversion.