Standard university or high-school physics teaching material on projectile motion is usually based on Newton's second law in vacuum, neglecting aerodynamics. We present a low-cost experiment for teaching projectile motion using the students' cell phones and sports equipment, which allows the students to test theory and numerical simulation against experimental data in the real world. For a shot put, theoretical predictions assuming projectile motion in vacuum agree with experimentally obtained trajectories in air to within a few centimeters. However, for a table tennis ball, vacuum trajectories can be almost three times as long as experimentally obtained trajectories. An equation of motion including the aerodynamic drag force has no analytic solution, but it is straightforward to integrate numerically for high-school or first-year university students. Accounting for aerodynamic drag substantially improves the match with experimental data for any ball. In a second experiment, balls are shot with spin resulting in curveball trajectories. Numerical simulations including the Magnus force can give accurate predictions of 3D curveball trajectories, both curving according to the normal and the inverse Magnus effect. Balls shot with topspin and backspin are also accurately modelled. Finally, we model the bounce of an arbitrarily spinning ball using linear and angular impulse-momentum theorems and coefficients of restitution in vertical and horizontal directions. We find agreement with experimental data to within centimeters.
Skip Nav Destination
Article navigation
November 2020
PAPERS|
November 01 2020
Flight and bounce of spinning sports balls
Jacob Emil Mencke;
Jacob Emil Mencke
Department of Physics, Technical University of Denmark
, Fysikvej, 2800 Kgs. Lyngby, Denmark
Search for other works by this author on:
Mirko Salewski
;
Mirko Salewski
a)
Department of Physics, Technical University of Denmark
, Fysikvej, 2800 Kgs. Lyngby, Denmark
Search for other works by this author on:
Ole L. Trinhammer;
Ole L. Trinhammer
Department of Physics, Technical University of Denmark
, Fysikvej, 2800 Kgs. Lyngby, Denmark
Search for other works by this author on:
Andreas T. Adler
Andreas T. Adler
Team Danmark, House of Sports
, Brøndby Stadion 20, 2605 Brøndby, Denmark
Search for other works by this author on:
a)
ORCID: 0000-0002-3699-679X.
Am. J. Phys. 88, 934–947 (2020)
Article history
Received:
March 20 2020
Accepted:
July 14 2020
Citation
Jacob Emil Mencke, Mirko Salewski, Ole L. Trinhammer, Andreas T. Adler; Flight and bounce of spinning sports balls. Am. J. Phys. 1 November 2020; 88 (11): 934–947. https://doi.org/10.1119/10.0001659
Download citation file:
Pay-Per-View Access
$40.00
Sign In
You could not be signed in. Please check your credentials and make sure you have an active account and try again.
Citing articles via
Ergodic Lagrangian dynamics in a superhero universe
I. L. Tregillis, George R. R. Martin
All objects and some questions
Charles H. Lineweaver, Vihan M. Patel
The most efficient thermodynamic cycle under general engine constraints
Christopher Ong, Shaun Quek
A story with twists and turns: How to control the rotation of the notched stick
Martin Luttmann, Michel Luttmann
The spinorial ball: A macroscopic object of spin-1/2
Samuel Bernard-Bernardet, Emily Dumas, et al.
Related Content
The effect of spin on the flight of a baseball
Am. J. Phys. (February 2008)
Transition from bouncing to rolling on a horizontal surface
Am. J. Phys. (August 2024)
Impact behavior of a superball
Am. J. Phys. (March 2015)
Scattering of a baseball by a bat
Am. J. Phys. (October 2006)
How to hit home runs: Optimum baseball bat swing parameters for maximum range trajectories
American Journal of Physics (November 2003)