Why did angular momentum get the letter L

Question

Note - this question was inspired by this questions on physics.SE.

Many (most) physical quantities are denoted with a single letter - latin or greek. For many, the letter chosen makes sense: $t$ for time, $m$ for mass, etc. Often the letter chosen either relates to the word for the quantity (in the language of the person first describing it, or Latin or Greek) or indeed the name of the discoverer. Occasionally, the letter is borrowed from another field with a similar use. For example, the letter $n$ is often used for counting natural numbers, and thus became associated with quantum numbers.

All of which leaves me to wonder: why did angular momentum get the letter $L$? I saw a few "answers" online that I found very unsatisfactory - that it related to "Left", or the right angle made between the velocity and position vectors... I suspect there is a deeper explanation but it has eluded me. I tried looking at some of the early descriptions by Newton, Hooke and Kepler but didn't find an answer.

Answer 1

I just want to comment that the agreement on letters, by which we write $\frac d{dt}\mathbf L=\mathbf M$ for the law of angular momentum, must have come very late -- after 1964. As evidence, note that it is still written

1. $\frac d{dt}\mathfrak N=\mathfrak M$ by Sommerfeld in Mechanik (1943, p.63);

2. $\frac d{dt}\mathbf M=\mathbf L$ by Sommerfeld in Mechanics (1952, p.72);

3. $\frac d{dt}\mathbf P=\mathbf M$ by Joos in Theoretical Physics (3rd edition, 1958, p.110);

4. $\frac d{dt}\mathbf M=\mathbf K$ by Landau-Lifshitz in Mechanics (1960, p.108);

5. $\frac d{dt}\mathbf H=\mathbf L$ by Truesdell (quoting Joos) in Whence the Law of Moment of Momentum? (1964);

6. $\frac d{dt}\mathbf M=\mathbf L$ by Truesdell in Die Entwicklung des Drallsatzes (1964), which is a translation of 5.

Thus, it's likely going to be impossible to attribute the choice of $\mathbf L$ to anyone in particular.

EDIT: Much more promising seems to be the hypothesis that the choice was first made in quantum mechanics, to denote orbital angular momentum. As evidence, we have the following nice unanimity:

1. $L_x = \frac1i\bigl(y\frac\partial{\partial z}-z\frac\partial{\partial y}\bigr)$ in Weyl, Gruppentheorie und Quantenmechanik (1928, p.167);

2. $L_x = -\frac1i\bigl(y\frac\partial{\partial z}-z\frac\partial{\partial y}\bigr)$ in Eckart, The Application of Group theory... (1930, p.350);

3. $\pmb{\mathsf L}_z = \frac1i\bigl(y\frac\partial{\partial x}-x\frac\partial{\partial y}\bigr)$ in Wigner, Gruppentheorie und ihre Anwendung... (1931, p.219);

4. $L_x = \frac1i\bigl(y\frac\partial{\partial z}-z\frac\partial{\partial y}\bigr)$ in van der Waerden, Die gruppentheoretische Methode... (1932, p.19);

5. $\pmb l_3 = \frac1i\bigl(x_1\frac\partial{\partial x_2}-x_2\frac\partial{\partial x_1}\bigr)$ in Pauli, Die allgemeinen Prinzipien der Wellenmechanik (1933, p.185);

6. $L_x = \frac h{2\pi i}\bigl(y\frac\partial{\partial z}-z\frac\partial{\partial y}\bigr)$ in Bauer, Introduction à la théorie des groupes... (1933, p.38).

The point was, of course, that the eigenvalue of $L_x^2+L_y^2+L_z^2$ would relate to the azimuthal quantum number already denoted $l$ — a letter choice which seems attributed by Sommerfeld (1926) to Russell and Saunders, by Russell et al. (1929) to Hund (1927, p.27), and by Hund (1925, p.347) to Heisenberg (1925, p.850)...