The first picture shows quite well how a Chinook's blade paths are inter meshed between the two rotor heads. Failure of one rotor will leave the other one flying unmolested for a maximum of 1/3 of an Nr!
It was a synchromesh problem that brought down a North Sea variant in 1986 with considerable loss of life and ultimately led to the North Sea operators switching aircraft types.
Having only had a 'wee shot' in one, I don't claim to be an expert. However one of my more qualified colleagues told me that they have to self impose a 5000 fpm ROC. The reason for this is that at any higher rates of climb and they would not be able to establish an autorotative 'rate of descent flow' through the blades before the Nr decayed to critical levels in the event of an engine or transmission failure.