The angular momentum paradox is one of the oldest debated issues for unconventional superconductors, or more specifically, a px + ipy chiral superconductor or superfluid. The theoretical arguments have seemed to converged recently at Nℏ/2 with numerous new calculations about the intrinsic orbital angular momentum of a $p_x+ip_y$ chiral superconductor. An experimental confirmation of the intrinsic orbital angular momentum has been hampered by device sensitivity limits. However, a micro-electro-mechanical systems (MEMS) gyroscope could provide a breakthrough method to sufficient sensitivity. Here we discuss the low temperature characteristics of a MEMS gyroscope, and the results of preliminary test runs using such devices are also presented.