The problem of the pendulum hanging at the periphery of a rotating carousel is a typical exercice that undergaduate students are often asked to solve in order to check their knowledge about uniform circular motion [1]. The point is to find the angle θ that the pendulum of mass m makes with the vertical, by assuming a constant angular frequency ω, and a length of the pendulum l negligible compared to the radius R of the carousel.
In this letter, we will show that a more accurate solution may be easily obtained using a first order expansion, and its precision will be checked by comparison with an exact solution that may be found analytically or numerically. Calculations should be practicable for students comfortable with Taylor series.