Contents 
We compute the mean first passage time (MFPT) for a Brownian particle inside a twodimensional disk with reflective boundaries and a small interior trap rotating at a constant angular velocity. For a given angular velocity, we determine the optimal radius of rotation that minimizes the average MFPT over the entire disk. Several distinct regimes are observed, depending on the ratio between the angular velocity and trap size, and several intricate transitions are analyzed using tools of asymptotic analysis and Fourier series. This simple geometry provides a good test case for future studies of MFPT with more complex trap motion. 
