4.2.2.1 So­lu­tion an­gub-a

Ques­tion:

If the an­gu­lar mo­men­tum in a given di­rec­tion is a mul­ti­ple of $\hbar$ $\vphantom0\raisebox{1.5pt}{$=$}$ 1.054 57 10$\POW9,{-34}$ J s, then $\hbar$ should have units of an­gu­lar mo­men­tum. Ver­ify that.

An­swer:

An­gu­lar mo­men­tum is lin­ear mo­men­tum, (mass times ve­loc­ity,) times nor­mal dis­tance from the axis. So its units are kg (m/s) m. Con­versely J s is N m s and N, a New­ton, is kg m/s$\POW9,{2}$, so J s is kg m$\POW9,{2}$/s, the same as the units of $\hbar$.