My CPU fan turns on and off?

Sooo recently got a notebook because of school and found that my fan runs and then turns off my laptop is not particularly warm, it is temp. Controlled don't know me very well

Before you notice that your laptop is getting warmer than usual, the built-in sensor feels it and switches the fan on and off in a temperature-controlled manner.

Yes is basically temperature controlled.

Is also with modern graphics cards so that the fans stay below 60 degrees

If the laptop does not need cooling because it is underwhelmed, the fan switches off

Yes, that's normal. Not all laptops get noticeably hot when the fan starts to spin.