Final answer:
The question asks about the number of rotations made by a ceiling fan before it was switched off, given that it halves its angular velocity while making 36 rotations. However, to provide an accurate answer, additional details on the fan's angular deceleration would be required, which are not provided.
Step-by-step explanation:
The student’s question concerns the number of rotations a ceiling fan makes before it is switched off, given that its angular velocity is halved during 36 rotations as it coasts to a stop. To solve this, we can use the concepts of angular kinematics, which are closely related to the broader study of rotational motion in physics. However, as the question stands, we would need additional information, such as the angular acceleration of the fan as it slows down, to calculate the initial number of rotations.
The related example problems provided hint at different aspects of angular motion, addressing subjects such as angular acceleration, moment of inertia, and angular momentum. For instance, calculating torque and using kinematic equations for rotational systems. However, with no specific data on deceleration for the ceiling fan, the determination of the exact number of rotations prior to deceleration is not feasible purely based on the information given.