勢(いきお)い

いきおい
noun, adverb
force, vigor, momentum
descriptive
1. force, vigor, energy
Physical or emotional strength and intensity.
勢(いきお)いよく走(はし)り出(だ)した。
He started running vigorously.
Water is flowing with great force.
The wind was so strong that my umbrella almost broke.
2. momentum, impetus
The force or speed gained by movement or progress.
勢(いきお)いに乗(の)る。
To ride the momentum.
Common expression
勢(いきお)い余(あま)って転(ころ)んだ。
I fell over from the momentum.
It picked up speed going down the hill.
3. influence, power
The capacity to affect others or events.
That company has a lot of influence.
I was overwhelmed by the young player's energy.
The opposition movement is gaining power.
4. naturally, inevitably
As a natural consequence (adverbial use).
仕事(しごと)が増(ふ)えると、勢(いきお)い時間(じかん)がなくなる。
When work increases, you inevitably run out of time.
Adverbial use
If the population declines, the economy will naturally shrink too.
Adverbial use
If you try to do everything alone, strain will inevitably build up.
Adverbial use

勢(いきお)い has a broad range of meanings centered on force, vigor, and momentum. It can function as both a noun and an adverb.

USAGE (as a noun):
1. Physical force/vigor: 水(みず)の勢(いきお)い (force of water)
2. Momentum/impetus: 勢(いきお)いに乗(の)る (ride the momentum)
3. Influence/power: 会社(かいしゃ)の勢(いきお)い (a company's power)

Common patterns

USAGE (as an adverb):
When used as an adverb, 勢(いきお)い means 'naturally' or 'inevitably' — something happens as a natural consequence.