to push / to nag
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to push
To shove forward impatiently and inconsiderately in a crowd or queue in order to get ahead faster.
An der Kasse haben alle Leute gedrängelt, um als Erste dranzukommen.
At the checkout, everyone was pushing to be the first to get served.
'Drängeln' (to push/nag) is related to the verb 'drängen' (to press, to push). The ending '-eln' often suggests a repeated action or one perceived as annoying, which fits the meaning of 'drängeln' well.
Bitte nicht drängeln, alle kommen an die Reihe.
Please don't push; everyone will get a turn.
You can tell from context whether 'drängeln' means physical pushing or impatiently urging someone on. If it's about a queue or a crowd, the physical meaning is intended. If it's about time or a task, the figurative meaning is intended.
In der U-Bahn drängeln die Leute immer zur Tür.
On the subway, people are always pushing toward the door.
In the meaning 'to push ahead in a line', the reflexive form 'sich vordrängeln' (to push in / cut in line) is used very often. This emphasizes that someone is giving themselves an unfair advantage.
Es ist unhöflich, sich an der Supermarktkasse vorzudrängeln.
It's rude to cut in line at the supermarket checkout.
In the meaning 'to urge someone on', 'drängeln' (to nag) is often used as a negative request in the imperative to ask someone to stop doing it.
Drängel nicht so, ich beeile mich ja schon!
Don't nag me like that, I'm already hurrying!
to urge / push
'drängen' and 'drängeln' can both mean that someone is putting pressure on someone or wants to move forward. 'drängen' is more general: you can urge someone to make a decision or push your way through a crowd. 'drängeln' sounds impatient and often inconsiderate. It fits especially in queues, in traffic, or when someone keeps saying that things should go faster. The words are easy to confuse because both have to do with hurry and pressure. However, 'drängeln' more strongly describes annoying or rude behavior.
An der Kasse drängelt ein Kunde, obwohl alle warten müssen.
At the checkout, a customer pushes ahead, even though everyone has to wait.
Vor dem Termin drängt mich meine Schwester zu einer schnellen Entscheidung.
Before the appointment, my sister urges me to make a quick decision.