N2 = HP compressor rotation speed.
During a gas turbine engine start, a pneumatic starter motor drives the low-pressure compressor to compress enough air to start the combustion and drive the turbines. There could be many problems during an engine start such as igniters malfunction, starter motor problem, shafts malfunction/damage, etc. N2 is the first spool being rotated during the engine start; it is the smallest, so it makes sense to start rotating the N2 first before the N1. This will also help to reduce the size and complexity of the starter motor that will not require rotating all the spools at the same time.
The two answers mentioning the hung start related to a fuel selection problem are wrong because the hung start is only caused by a too low pneumatic pressure before fuel is supplied to sustain combustion and nothing else.
“No N2 rotation, although N1 may accelerate normally” makes no sense for the reason explained above. N1 (the fan and LP compressor-turbine spool) cannot rotate if there’s no N2 rotation.
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