The motion of a coin falling to the bottom of a tank filled with liquid can be remarkably similar to the fluttering and tumbling of a falling autumn leaf. Investigate how the motion of the coin depends on relevant parameters.

Background reading from IYPT reference kit

Autumn coin (youtube, Никита Черников, 06.07.2025), https://youtu.be/EW6tA00SZL8 Autumn coin - top (YouTube, Никита Черников, 06.07.2025), https://youtube.com/shorts/ItA7Z667tYc Coins Dropped Into Crystal Clear Water: A View From The Bottom As The Coins Sink. Ogemaw Springs, MI (youtube, Chosen Won, 01.02.2021), https://youtu.be/jx0acGK7NC8 Wikipedia: Angle of attack, https://en.wikipedia.org/wiki/Angle_of_attack Wikipedia: Froude number, https://en.wikipedia.org/wiki/Froude_number Wikipedia: Free fall, https://en.wikipedia.org/wiki/Free_fall Wikipedia: Drag, https://en.wikipedia.org/wiki/Drag_(physics)

*A. Tinklenberg, M. Guala, and F. Coletti. Thin disks falling in air. J. Fluid Mech. 962, A3 (2023), https://doi.org/10.1017/jfm.2023.209 *L. Heisinger, P. Newton, and E. Kanso. Coins falling in water. J. Fluid Mech. 742, 243-253 (2014), https://doi.org/10.1017/jfm.2014.6 *D. M. Hargreaves, B. Kakimpa, and J. S. Owen. The computational fluid dynamics modelling of the autorotation of square, flat plates. J. Fluids Struct. 46, 111-133 (2014), https://doi.org/10.1016/j.jfluidstructs.2013.12.006

*A. Andersen, U. Pesavento, and Z. J. Wang. Unsteady aerodynamics of fluttering and tumbling plates. J. Fluid Mech. 541, 1, 65-90 (2005), https://doi.org/10.1017/S002211200500594X, https://dragonfly.tam.cornell.edu/publications/S002211200500594Xa.pdf *U. Pesavento and Z. J. Wang. Falling paper: Navier-Stokes solutions, model of fluid forces, and center of mass elevation. Phys. Rev. Lett. 93, 14, 144501 (2004), https://doi.org/10.1103/PhysRevLett.93.144501 *S. B. Field, M. Klaus, M. G. Moore, and F. Nori. Chaotic dynamics of falling disks. Nature 388, 252-254 (1997), https://doi.org/10.1038/40817, https://public.websites.umich.edu/~nori/disks/long.pdf