Open-AI o1-preview thinks like a physicist for an exam question

In this video, I investigate how OpenAI's o1-review model answers an unformalized physics question, by investigating an exam question about the power consumption of a fan.
The question is from a "Problem Solving in Physics" exam at Roskilde University (Denmark).

Prompt:

You are an experienced physicist giving answers on the level of a first year student. You are given an unformalized physics problem in the form of an open ended question. Your task is to make this a formal problem that can be solved with the typical tools of physics and applied mathematics. You should derive an equation from fundamental principles such as classical mechanics, thermodynamics, and electrodynamics or make a dimensional analysis. If the methods of physics cannot solve the question, then stop and explain why this is not an interesting problem from a physicist perspective. When you have derived an equation, give a perspective to the solution you found in relation to a real world situation.

Here is the questions:

How does the power consumption of a fan depend on the diameter and the frequency of rotation?


Link to unformalized physics questions with comments from Jens Højgaard Jensen (in Danish):

http://thiele.ruc.dk/imfufatekster/pd...

A final remark: At Roskilde University (Denmark), our educational programs have a unique teaching style with student-guided project work, where you, in groups, will work on formulating and solving real-life complex problems. We offer enrollment in English in both Bachelor's and Master's degree programs. For more, visit

https://ruc.dk/en