Self-Plagiarism
"Self-plagiarism is defined as a type of plagiarism in which the writer republishes a work in its entirety or reuses portions of a previously written text while authoring a new work. Writers often maintain that because they are the authors, they can use the work again as they wish; they can’t really plagiarize themselves because they are not taking any words or ideas from someone else. But while the discussion continues on whether self-plagiarism is possible, the ethical issue of self-plagiarism is significant, especially because self-plagiarism can infringe upon a publisher’s copyright. Traditional definitions of plagiarism do not account for self-plagiarism, so writers may be unaware of the ethics and laws involved in reusing or repurposing texts."
From "Is Recycling Your Own Work Plagiarism?" Turnitin, LLC. https://www.turnitin.com/blog/is-recycling-your-own-work-plagiarism. Accessed 2017.
While it sounds like it should be okay, reusing your work it is actually considered plagiarism because you are presenting the paper as new work for another teacher. Even if the topic fits the assignment, you should be building on previous knowledge as you go through college.
image from DenBleyke, Rob. 2010. Cyanide & Happiness (Explosm.net). Accessed 2017.