покача́ть

fairly common #2087C1

verbperfective imperfective is кача́ть

1.
to shake (one's head), to give a shake
Он молча покача́л голово́й.
He silently shook his head.
Most often with головой; expresses doubt or refusal.
2.
to rock (for a while), to swing (for a while), to dandle
Покача́й малыша́, он ско́ро уснёт.
Rock the baby a little, he'll fall asleep soon.
Perfective of a short action: a baby, a cradle, a branch.
3.
to pump (for a while)
Мы покача́ли во́ду из коло́дца.
We pumped some water from the well.
Of liquid, gas, air.
4.
to downloadcomputing
Покача́й мне пару фи́льмов на выходные.
Download me a couple of films for the weekend.
Colloquial, of data or files.

Examples

Мать, разнимавшая детей, покачала головой.
The mother who had separated the children shook her head.
Медсестра, разбинтовывавшая повязку, покачала головой.
The nurse, who was removing the bandage, shook her head.
Том улыбну́лся и покача́л голово́й.
Tom smiled and shook his head.
Мужчина, взвешивавший чемодан, покачал головой.
The man who was weighing the suitcase shook his head.
Мальчик недовольно покачал головой
The boy shook his head unhappily.
Друг, усмехнувшийся моей шутке, покачал головой.
The friend who smirked at my joke shook his head.
Я отрицательно покача́л голово́й.
I shook my head no.
Присвистнувший от удивления сосед покачал головой.
The neighbor, who whistled briefly in surprise, shook his head.

Imperative
ты	покача́й
вы	покача́йте

Active present	-
Active past	покача́вший	having swayed, having rocked, having shaken (a bit)
Passive present	-
Passive past	пока́чанный	swung, rocked, swayed
Gerund present	-
Gerund past	покача́в покачавши	while doing (past)

кача́тьto rock; to shake (one's head); to pump; to download
verbimperfective
вкача́тьto pump in; to pump in (money); to upload
verbperfective
укачатьto rock to sleep; to make sick (from motion); to rock back and forth
verbperfective
вы́качатьto pump out
verbperfective
докача́тьto pump up (fully); to finish downloading
verbperfective