Newton's Rotating Water Bucket: A Simple Model

Abstract

Isaac Newton proposed hanging a bucket of water by a cord in the Principia. If the cord is twisted and the bucket is then released, it begins to spin and the surface of the water acquires a paraboloidal shape. In this paper, the parabolic profile as a function of the angle of rotation is derived, as well as the period of the torsional oscillations as a function of the initial parameters of the system.

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Document Details

Document Type
Technical Report
Publication Date
Jan 01, 2013
Accession Number
ADA592010

Entities

People

  • Carl E. Mungan
  • Trevor C. Lipscombe

Organizations

  • United States Naval Academy

Tags

Communities of Interest

  • Energy and Power Technologies
  • Ground and Sea Platforms

DTIC Thesaurus Topics

  • Abstracts
  • Angular Acceleration
  • Boundary Layer
  • Centrifugal Force
  • Energy
  • Equations
  • Gravitational Fields
  • Integrals
  • Kinetic Energy
  • Moment Of Inertia
  • Numbers
  • Oscillation
  • Potential Energy
  • Rotation
  • Shape
  • Square Roots
  • United States Naval Academy

Readers

  • Aerodynamics.
  • Control Systems Engineering.
  • Materials Science