a/the

[theol]

I am a hamster. I love to run on a hamster wheel.
I am a hamster. I love to run on the hamster wheel.

which one is correct?

 

[Skrej]

Both are correct.

 

[emsr2d2]

I am a hamster. I love to run on a hamster wheel.
I am a hamster. I love to run on the hamster wheel.

Which one is correct?

There's no need to specify "hamster wheel". You've already introduced the idea of a hamster so readers/listeners will know what kind of wheel you're talking about.