Learn Hardcore Korean: undongeul hago naseo pari pigonhaeyo.

운동 means “exercise,” and 하다 means “to do.” In 운동을 하고 나서, -고 is the connective form of a verb (here 하다) and 나서 attaches to that to express “after doing.” So literally it’s “after doing exercise,” i.e. “after exercising.”

How does -고 나서 differ from -고 나면?

-고 나서 indicates a sequence: “after A happens, then B happens.”
Example: 운동을 하고 나서 샤워했어요 (“I took a shower after exercising”).
-고 나면 is conditional/blind future: “if/when after A happens, then B will follow (as a general rule).”
Example: 운동을 하고 나면 기분이 좋아져요 (“When/if I exercise, I feel better [in general]”).

Why is 을 used after 운동 in 운동을 하고 나서?

Because 운동 is the direct object of 하다 (“to do exercise”). You always mark a verb’s object with 을 or 를. Since 운동 ends in a consonant, you use 을 (운동을 하다).

Why is 이 used after 팔 instead of 가 in 팔이 피곤해요?

이/가 are subject markers. When a noun ends in a consonant (here 팔 ends in ㄹ), you attach 이. If the noun ends in a vowel, you attach 가.

Could we say 팔은 피곤해요 instead of 팔이 피곤해요? What’s the difference?

Yes, it’s grammatically possible, but nuance changes.

팔이 피곤해요 simply states “My arms are tired”, focusing on the fact.
팔은 피곤해요 uses 은 (topic marker), roughly “As for my arms, they’re tired,” which might imply contrast (e.g. “but my legs aren’t”). Use 이/가 to introduce new information as the grammatical subject.

Why is 피곤해요 used here and how is it conjugated?

피곤하다 is a descriptive verb (an adjective) meaning “to be tired.” The stem is 피곤하-. In polite speech you drop -다 and add -해요, giving 피곤해요, i.e. “(they) are tired” or “I’m tired.”

What’s the difference between 피곤해요 and 피곤해졌어요?

피곤해요 states a current state: “(I/my arms) am/are tired.”
피곤해졌어요 uses -아/어지다 to express a change of state: “(I/my arms) became tired.”
Use -해요 for simple description, -해졌어요 to emphasize you weren’t tired before but are now.

Could we replace 운동을 하고 나서 with 운동 후에 or 운동을 한 후에? What’s the nuance?

All three mean “after exercising,” but differ in style:

운동 후에 is the most concise (noun + postposition). Often in writing or formal speech.
운동을 한 후에 uses a relative clause (“the exercise that was done”) + 후에. Neutral, slightly more formal.
운동을 하고 나서 emphasizes the action–sequence relationship (“do exercise, and then…”). Common in conversation. You’ll also hear 운동하고 나서 (dropping the object marker).

Why use 하고 instead of 해서 in 운동을 하고 나서 팔이 피곤해요?

-고 is the plain connective needed for -고 나서 (“after doing…”) to work.
해서 is the -아/어서 form of 하다, which often implies cause (“because”) or general connection (“so”). If you said 운동을 해서 팔이 피곤해요, it means “Because I exercised, my arms are tired,” not specifically “after … then ….” To express strict sequence, you need -고 나서.