The moment map of the action of $\operatorname{SO}(3)$ on the sphere can be thought of as inclusion from $S^2$ into $\mathbb R^3$ by identifying $\mathfrak{so}(3)$ (the Lie algebra of $\operatorname{SO}(3)$) with $\mathbb R^3$.
I am just learning symplectic geometry and this fact came up without explanation in a paper that I'm reading. Can someone explain this, preferably in an intuitive way?
Thanks!