Maximum range of a projectile thrown from constant-speed circular motion

TL;DR

This paper analyzes the maximum range of a projectile launched from a rotating arm, exploring how initial position and throwing method affect the maximum distance, with detailed calculations confirming conceptual insights.

Contribution

It introduces a detailed analysis of projectile range from a rotating arm, extending standard projectile motion problems to more complex rotational scenarios.

Findings

Maximum throw distance depends on initial position and throw angle.

Underhand and overhand throws have different optimal angles.

Calculations confirm conceptual predictions about projectile range from rotating motion.

Abstract

The problem of determining the angle at which a point mass launched from ground level with a given speed is a standard exercise in mechanics. Similar, yet conceptually and calculationally more difficult problems have been suggested to improve student proficiency in projectile motion. The problem of determining the maximum distance of a rock thrown from a rotating arm motion is presented and analyzed in detail in this text. The calculational results confirm several conceptually derived conclusions regarding the initial throw position and provide some details on the angles and the way of throwing (underhand or overhand) which produce the maximum throw distance.