Given that both have the same dimensions, it is a fact that Planck’s constant and angular momentum are comparable.
E = hv
where the frequency dimensions are the inverse of the time period, or T−1, and the energy dimensions, E, are ML2T−2.
Therefore, ML2T−2=[h]T−1
or [h]=ML2T−1
Angular momentum, L=Iω, now
where radian is dimensionless and omega units are the inverse of time (rad/sec).
Since I is of the form kMx2, its units are ML2.
Consequently, [L]=ML2T−1; T-1 due to rad/sec, which would leave T-1 since radians don’t have dimensions.
Given that both have the same dimensions, it is a fact that Planck’s constant and angular momentum are comparable.
E = hv
where the frequency dimensions are the inverse of the time period, or T−1, and the energy dimensions, E, are ML2T−2.
Therefore, ML2T−2=[h]T−1
or [h]=ML2T−1
Angular momentum, L=Iω, now
where radian is dimensionless and omega units are the inverse of time (rad/sec).
Since I is of the form kMx2, its units are ML2.
Consequently, [L]=ML2T−1; T-1 due to rad/sec, which would leave T-1 since radians don’t have dimensions.