Asking, caring and fighting with 'um'
When you ask for a favor, look after a child, or mourn a loss, English uses a whole mix of prepositions like "for", "after", and "over". Sometimes, English uses no preposition at all. German is surprisingly consistent here. A specific group of verbs expressing requests, care, and struggle all pair up with the preposition um.
Because English translates these connections so differently, you cannot rely on word-for-word translation. You simply have to memorize that verbs like bitten and sich kümmern demand um followed by the accusative case.
Let us start with requesting things. If you want to ask someone for something, the verb bitten is your go-to choice. The person you are asking is in the accusative case, and the thing you want is introduced by um. The same rule applies when things get more desperate with verbs like betteln.
When you direct your care or effort toward someone or something, um appears again. A very common verb you will use daily is sich kümmern. You can use it when you are looking after a person, or when you are taking care of a task or problem. Another great verb in this category is sich bemühen, which you use when you are trying hard to get or achieve something.
You might also hear native speakers use verbs like sich sorgen (to worry) in the exact same way.
The preposition um is also used when you are fighting for a goal or mourning a loss. For example, the verb kämpfen can be combined with several prepositions depending on the context. You can fight against someone or with someone, but when you want to name the contested objective you are trying to win or keep, you use kämpfen um. Finally, when someone passes away, you use trauern um to express who is being mourned.
Instead of guessing which preposition matches the English translation, remember this pattern. When a German verb describes asking, caring, struggling, or mourning, it very likely takes um and the accusative case to show the objective of that action.