  For a Lie groupoid $\mathcal{G}$ with Lie algebroid $A$, we realize the
symplectic leaves of the Lie-Poisson structure on $A^*$ as orbits of the affine
coadjoint action of the Lie groupoid $\mathcal{J}\mathcal{G}\ltimes T^*M$ on
$A^*$, which coincide with the groupoid orbits of the symplectic groupoid
$T^*\mathcal{G}$ over $A^*$. It is also shown that there is a fiber bundle
structure on each symplectic leaf. In the case of gauge groupoids, a symplectic
leaf is the universal phase space for a classical particle in a Yang-Mills
field.
