1Q10.30 - Moments of Inertia - Hoops and Disks

Code Number:
1Q10.30
Demo Title:
Moments of Inertia - Hoops and Disks
Condition:
Good
Principle:
Exchange of Potential and Kinetic Energy, Moments of Inertia
Area of Study:
Mechanics
Equipment:
Wood & Metal Disks (Asst.) (Equal Mass), Inclined Plane, and Stop Block.
Procedure:

Video Credit: Jonathan M. Sullivan-Wood.

The only assembly required is to raise one end of the incline up with blocks until the desired angle is achieved.  Some type of stop is then attached to the end of the table so that the disks do not roll off the table after rolling down the incline.

Objects with different numerical coefficients for the moments of inertia may also be rolled down an incline.  The set we have has a hoop, a cylinder, a uniform density ball, a cone, and an object with the mass concentrated in the center.  All of these objects have the same rolling diameter.  The order of these objects will be from slowest to fastest: hoop, cylinder, ball, cone, and center concentrated.  Note that the cone and center concentrated have low mass hoops attached so that they also have the same rolling diameter as the other objects.

References:
  • Jinhui Wang and Bernard Ricardo, "Squashing Method for Moment of Inertia Calculations", TPT, Vol. 57, #8, Nov. 2019, p. 551. 
  • Terry Toepker, "Combo of Figuring Physics", TPT, Vol. 57, #6, Apr. 2019, p. 356.
  • Paul Hewitt, "Figuring Physics March 2019 Answer", TPT, Vol. 57, #4, Apr. 2019, p. 259.
  • V. L. B. de Jesus and D. G. G. Sasaki, "A Simple Experiment to Determine the Moments of Inertia of the Fidget Spinner by Video Analysis", TPT, Vol. 56, #9, Dec. 2018, p. 639.
  • Matthaios Patrinopoulos and Chrysovalantis Kefalis, "Angular Velocity Direct Measurement and Moment of Inertia Calculation of a Rigid Body Using a Smartphone", TPT, Vol. 53, #9, Dec. 2015, p. 564.
  • "Errata", TPT, Vol. 53, #9, Dec. 2015, p. 516.
  • Joseph A. Rizcallah, "Moment of Inertia by Differentiation", TPT, Vol. 53, #8, Nov. 2015, p. 482.
  • Rod Cross, "Precession of a Spinning Ball Rolling Down a Inclined Plane", TPT, Vol. 53, #4, Apr. 2015, p. 217.
  • Seok-Cheol Hong and Seok-In Hong, "Moments of Inertia of Disks and Spheres Without Integration", TPT, Vol. 51, #3, Mar. 2013, p. 139.
  • Jordi Solbes and Francisco Tarín, "Which Reaches the Bottom First?", TPT, Vol. 46, #9, Dec. 2008, p. 550.
  • Takao Takeuchi, "The Moment of Inertia of a Rectangular Rod", TPT, Vol. 45, #8, Nov. 2007, p. 518.
  • Stephen Van Hook, Adam Lark , Jeff Hodges, Eric Celebrezze, Lindsey Channels, "Playground Physics: Determining the Moment of Inertia of a Merry-Go-Round", TPT, Vol. 45, # 2, Feb. 2007, p. 85.
  • Benjamin Oostra, "Moment of Inertia Without Integrals", TPT, Vol. 44, #5, May 2006, p. 283.
  • Adam Niculescu, "A Rolling Sphere Experiment", TPT, Vol. 44, #3, Mar. 2006, p. 157.
  • Paul Hewitt, "Figuring Physics: Up the Incline", TPT, Vol. 43, #9, Dec. 2005, p. 572.
  • Robert Shafer, "Downhill Races Revisited", TPT, Vol. 42, #6, Sept. 2004, p. 324.
  • Cruse Melvin, "Correction: 'Downhill Races' [Phys. Teach. 40(4) 222 (2002)]", TPT, Vol. 40, #6, Sept. 2002, p. 325.
  • Cruse Melvin, "Downhill Races", TPT, Vol. 40, #4, Apr. 2002, p. 222.
  • Ian Thomas, "Another Rolling Paradox", TPT, Vol. 32, # 4, April 1994, p. 200.
  • Terrence P. Toepker, "Galileo's Damped Oscillator", TPT, Vol. 31, #9, Dec. 1993, p. 537.
  • Carl R. Stannard, Thomas P. O'Brien, and Andrew J. Telesca, Jr., "A Ball with Pure Translation Motion?", TPT, Vol. 30, #9, Dec. 1992, p. 526.
  • Kaye M. Elsner, "Dispense With Misconceptions About Inertia: Have A Race!", TPT, Vol. 30, #2, Feb. 1992, p. 108.
  • Walter Connolly and R. B. Knollenberg III, "An Apparatus for Demonstrating Energy Conservation", TPT, Vol. 27, #2, Feb. 1989, p. 110.
  • Robert H. March, "Who Will Win the Race?", TPT, Vol. 26, #5, May 1988, p. 297.
  • J. Sherfinski, "Acceleration from the Energy Function Derivative", TPT, Vol. 26, #4, Apr. 1988, p. 228.
  • Richard Guglielmino, "Rotational Dynamics Labs", TPT, Vol. 23, #3, Mar. 1985, p. 166.
  • R. D. Edge, "The Errant Pool Balls", TPT, Vol. 20, #1, Jan. 1982, p. 50.
  • Mario Iona, "Friction When Rolling", TPT, Vol. 19, #3, Mar. 1981, p. 154.
  • Brother James Mahoney, "An Exercise in Rotational Motion", TPT, Vol. 18, #8, Nov. 1980, p. 600.
  • Lyle F. Minkler, "Measuring the Moment of Inertia of an Airplane", TPT, Vol. 13, #1, Jan. 1975, p. 46.
  • Manoug Ansour, "A Simple Method for Solving Problems Involving Moment of Inertia and Acceleration", TPT, Vol. 8, #5, May 1970, p. 267.
  • Clinton Thomas, "Loading a Disk for Mechanics Demonstration", TPT, Vol. 5, #6, Sept. 1967, p. 287.
  • Johan Linden, Kjell-Mikael Kallman, Markus Lindberg, "The Rolling Elliptical Cylinder", AJP, Vol. 89, #4, April 2021, p. 358.
  • I. W. Griffiths, J. Watkins, and D. Sharpe, "Measuring the Moment of Inertia of the Human Body by a Rotating Platform Method", AJP, Vol. 73, #1, Jan. 2005, p. 85.
  • Colin P. Ratcliffe, "The 3:4:5 Coincidence of an Optimized Moment of Inertia Classroom Demonstration", AJP, Vol. 65, #10, Oct. 1997, p. 1015.
  • A. Tan, "The Moment of Inertia of a Basketball", AJP, Vol. 53, #9, Sept. 1985, p. 811.
  • Bruce Eaton, Richard DeGeer, and Walter Johnson, "Moment of Inertia Apparatus", AJP, Vol. 53, #2, Feb. 1985, p. 183.
  • Freier and Anderson, "Ms-1, 3", A Demonstration Handbook for Physics.
  • "M-678. Hoop, Disk, and Sphere Race", DICK and RAE Physics Demo Notebook.
  • Robert Ehrlich, "E.2, Rolling Disks, Hoops, and Spheres Down an Incline", Turn the World Inside Out, p. 52.
  • Vicki Cobb and Kathy Darling, "An Unbeatable Fast Ball", Bet You Can't!.
  • Borislaw Bilash II and David Maiullo, "Race of Shape", A Demo a Day: A Year of Physics Demonstrations, p. 164.
  • Julien Clinton Sprott, "1.9, Inclined Plane", Physics Demonstrations, ISBN 0-299-21580-6, p. 23.
  • "5.2.5. Linear and Rotational Kinetic Energy", Cunningham and Herr, Hands - On Physics Activities with Real Life Applications.
  • Christopher P. Jargodzki and Franklin Potter, "239, "And the Winner Is...", Mad About Physics, p. 95, 231.
  • Brown, Science for You - 112 Illustrated Experiments.
  • "Downhill Race", Exploratorium Science Snackbook Series, "Force and Motion".
  • Janice VanCleave, "Shape Up", 201 Awesome, Magical, Bizarre, & Incredible Experiments, p. 104.
  • Ron Hipschman, "Downhill Race", Exploratorium Cookbook III, p. 136-1 - 136-3.
  • Julius Sumner Miller, Q62 & A62, Millergrams I – Some Enchanting Questions for Enquiring Minds, p. 42 & 99.
  • Julius Sumner Miller, Q123 & A123, Millergrams II – Some More Enchanting Questions for Enquiring Minds, p. 16 & 79.














Disclaimer: These demonstrations are provided only for illustrative use by persons affiliated with The University of Iowa and only under the direction of a trained instructor or physicist.  The University of Iowa is not responsible for demonstrations performed by those using their own equipment or who choose to use this reference material for their own purpose.  The demonstrations included here are within the public domain and can be found in materials contained in libraries, bookstores, and through electronic sources.  Performing all or any portion of any of these demonstrations, with or without revisions not depicted here entails inherent risks.  These risks include, without limitation, bodily injury (and possibly death), including risks to health that may be temporary or permanent and that may exacerbate a pre-existing medical condition; and property loss or damage.  Anyone performing any part of these demonstrations, even with revisions, knowingly and voluntarily assumes all risks associated with them.