Suppose the population has been growing at a rapid clip, like in Liberia.
Then you will have a situation where the grandparent generation will have less population than the parents and the parents will be fewer than the children, e.g.:
2 80 year olds
6 60 year olds
15 40 year olds
40 20 year olds
100 babies
--------
163 people
One woman 80 year old had six babies with her husband. The three women in the next generation bore 15 babies. With a fertility rate around five, you will have a population pyramid where the babies outnumber the 80 year olds by about 50 to 1.
Then if fertility suddenly drops down to replacement level, the babies will eventually grow up to be 80 year olds in a country where the size of each generation is equal, e.g.:
100 80 year olds
100 60 year olds
100 40 year olds
100 20 year olds
100 babies
-----
500 people
So there's one more quadrupling (approximately) built in to the system even after the birth rate gets under control. Since the birth rate might not get under control until the resources run out in famine, war, or epidemic, we may be looking at a situation where high fertility countries are destined to have not only more people than they can support, but four times as many as they can support and chronic disasters for humanity. The only relief is thinking ahead and family planning, which is not necessarily our strong point as a species.
Say the population has been growing fast so most people are aged 0-20, and then the fertility rate drops to 2.1. Over the next 25 years you still have a lot of kids born while those people grow up, while there will not be many deaths because there will not be many old people to die off.
What? Can you explain this? Sorry if it's obvious, but I can't seem to grasp what you mean by population momentum.