We report optical observations of the luminous blue variable (LBV) HR Carinae which show that the star has reached a visual minimum phase in 2009. More importantly, we detected absorptions due to SiIV λλ4088-4116. To match their observed line profiles from 2009 May, a high rotational velocity of v rot ≃ 150 ∼ 20 km s<SUP>-1</SUP> is needed (assuming an inclination angle of 30°), implying that HR Car rotates at ≃0.88 ∼ 0.2 of its critical velocity for breakup (v<SUB>crit</SUB>). Our results suggest that fast rotation is typical in all strong-variable, bona fide galactic LBVs, which present S-Dor-type variability. Strong-variable LBVs are located in a well-defined region of the HR diagram during visual minimum (the "LBV minimum instability strip"). We suggest this region corresponds to where v crit is reached. To the left of this strip, a forbidden zone with v<SUB>rot</SUB>/v<SUB>crit</SUB>>1 is present, explaining why no LBVs are detected in this zone. Since dormant/ex LBVs like P Cygni and HD 168625 have low v rot, we propose that LBVs can be separated into two groups: fast-rotating, strong-variable stars showing S-Dor cycles (such as AG Car and HR Car) and slow-rotating stars with much less variability (such as P Cygni and HD 168625). We speculate that supernova (SN) progenitors which had S-Dor cycles before exploding (such as in SN 2001ig, SN 2003bg, and SN 2005gj) could have been fast rotators. We suggest that the potential difficulty of fast-rotating Galactic LBVs to lose angular momentum is additional evidence that such stars could explode during the LBV phase.Instituto de Astrofísica de La PlataFacultad de Ciencias Astronómicas y Geofísicas