I'm taking a dynamics class where we are specifically focusing on the transport theorem. I need to first identify the position vector, and then take 2 derivatives for inertial velocity and inertial acceleration. While I understand how that works, there's one step in the solution to the problem below that I do not currently follow.
The image link below is the worked solution to the problem.
Worked correct solution to the above problem statement.
While I understand the concept as a whole, there's one step that my professor didn't go into much detail about, which is the focus of this post. I shared a screenshot below focusing on the s_\alpha portion but the derivation of s_r based on the E-Frame is also confusing.
E-frame with s alpha vector relationship
Could someone help me out with a quick explainer on how to derive these vectors from components of the E-Frame?