Planck's constant has the dimensions (unit) of:

We define energy of a photon E=h f, here h is Planck's constant and f is the frequency.h=Ef⇒[h]=[E][f]=ML2 T-2T-1=ML2 T-1We define angular momentum as L=Iω⇒[L]=[I][ω]=ML2T−1=ML2T−1Hence =  [h]=[L]=ML2T-1