Far East Journal of Mathematical Education

The Far East Journal of Mathematical Education is a peer-reviewed journal focused on mathematical education. It publishes research papers that enhance understanding of mathematical concepts and encourages the use of technology, statistics, algorithms, and simulations in mathematics learning.

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DISTINCTION BETWEEN VECTOR AND COORDINATE SYSTEM INVERSIONS BASED ON MECHANICAL EXAMPLES

Authors

  • Yukio Kobayashi

Keywords:

vector inversion, coordinate system inversion, angular momentum, vector product, polar vectors, axial vectors

DOI:

https://doi.org/10.17654/0973563126004

Abstract

Polar vectors, such as displacement, velocity, and force vectors, and axial vectors, including area, angular momentum, and angular velocity vectors, indicate different conversion rules for their components regarding inversion. The distinction between the inversion of a vector and that of a coordinate system is important; however, they are related through the expressions of the component transformation laws. In both inversion types, the signs of the components of inversed vectors depend on the definition of the vector product. Inversion of the angular momentum vector of an axial vector represents another approach for expressing the law of conservation of angular momentum for constant-velocity circular motion.

Received: October 6, 2025
Accepted: October 27, 2025

References

[1] H. Ando, Nature of axial vector, The Astronomical Herald 112 (2019), 255-256. (in Japanese).

[2] K. Gotô, Butsurigaku no Kiso Joshiki Kyoritsu-pub 1985 (in Japanese).

[3] Y. Kobayashi, Alternative method for introducing torque and angular momentum, Journal of Physics Education (IAPT) 32(1) (2016), Article Number 3.

[4] D. Liu and Y. Kottegoda, Disconnect between undergraduates’ understanding of the algebraic and geometric aspects of vectors, European Journal of Physics 40 (2019), 035702.

[5] A. Fanzi, K. R. Kawuri and R. Pratiwi, Multi-perspective views of students’ difficulties with one-dimensional vector and two-dimensional vector, J. Phys.: Conf. Sec. 795 (2017), 012054.

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Published

12-12-2025

Issue

Vol. 28 No. 1 (2026)

Section

Articles

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How to Cite

DISTINCTION BETWEEN VECTOR AND COORDINATE SYSTEM INVERSIONS BASED ON MECHANICAL EXAMPLES. (2025). Far East Journal of Mathematical Education, 28(1), 15-29. https://doi.org/10.17654/0973563126004

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