A theoretical and experimental investigation of the rotational dynamics, including friction, of a slamming door is presented. Based on existing work regarding different damping models for rotational and oscillatory motions, we examine different forms for the (angular) velocity dependence (ωn, n = 0, 1, 2) of the frictional force. An analytic solution is given when all three friction terms are present and several solutions for specific cases known from the literature are reproduced. The motion of a door is investigated experimentally using a smartphone, and the data are compared with the theoretical results. A laboratory experiment under more controlled conditions is conducted to gain a deeper understanding of the movement of a slammed door. Our findings provide quantitative evidence that damping models involving quadratic air drag are most appropriate for the slamming of a door. Examining this everyday example of a physical phenomenon increases student motivation, because they can relate it to their own personal experience.
Note that we can restrict our considerations to scalars because all vector quantities such as torque, angular velocity, or frictional forces are assumed to be either parallel or pairwise perpendicular to each other. Furthermore, note that τf is a composite of the friction at the hinges (constant torque) and air drag (linear and quadratic air drag).
While the determination of ω0 from the graph seems appropriate in our case (cf. Sec. III A), this procedure can negatively affect the reliability of our conclusions; a lot of variance on the coefficients a, b, and c will be consumed by freedom on ω0.