Is my bathroom extractor fan broken?

My bathroom extractor fan is switched on when the main bathroom light is switched on.
However, I don't use this light often so the fan hasn't ben used a great deal.
Recently, I have had to use this light as our other bathroom light was broken (I haven't been very lucky!)

Anyway, the fan still moves, but v slowly. ...and then after a few minutes, it just stops. After which I turn the light/extractor off. ...and I am not entirely sure, but I think I can smell warm plastic. Not good is it.

So do you think the extractor is broken? If so, is there a way to fix it, or is it better/quicker/easier to buy and fix a new one.

Thanking you in advance
Amanda