Understanding and Solving the Rubik's Cube Without Algorithms
For rotations of the inner layers (M, E, and S), the WCA used to use the same letters, but now it only uses the notation to rotate two layers simultaneously. The letter 'w' is always added in front of the desired outer layer letter, indicating that this layer and the inner layer are rotated simultaneously. For example, Rw indicates that the R layer and the M layer are rotated in the direction of R.
This means that to indicate the rotation of only one inner layer, such as M, it is necessary to use two notations: one indicating the rotation of two layers and the other indicating the rotation of the outer layer back to its original position. Suppose you want to indicate the rotation of the M layer alone in the direction of R, then you would need to write: Rw R'. That is, both layers (R and M) are rotated in the direction of R, and then only layer R returns to the original position. Thus, there are equivalent notations. For example, M' is equivalent to Rw R' or Lw' L, as exemplified in Figures 3.15, 3.16, and 3.17. Again, you can click on play (â–·) to see them in action.
Note: In old notations, M followed the direction of L, S followed the direction of F, and E followed the direction of U.
App source: animcubejs.cubing.net/animcubejs.html