The Hopping Hoop (ILAP)

Physical Concepts Examined:
1. Motion
2. Friction

Table of Contents:

INTRODUCTION
Exercise 1: Center of Mass

PROBLEM STATEMENT AND ASSUMPTIONS

OVERVIEW OF THE SOLUTION PROCEDURE

CONSTRAINED MOTION: ROLLING WITHOUT SLIPPING
Exercise 2: Cycloid Constraint

SOME BASIC PHYSICS
Exercise 3: Center of Mass Equations of Motion
Exercise 4: Equation of Rotational Motion
Exercise 5: Derivation of the Equation of Energy Conservation
Exercise 6: Energy Conservation Equation in Terms of Theta Only
Exercise 7: Moment of Inertia of the Asymmetrically Weighted Hoop
Exercise 8: Mechanical Energy
Exercise 9: Motion on the Cycloid: Numerical Solution for a Typical Case
Exercise 10: Motion on the Cycloid: Analytic Solution for a Special Case
Exercise 11: Explicit Expressions for the Forces of Constraint

REMOVING ONE CONSTRAINT: ROLLING WITH SLIPPING
Exercise 12: Why the Hoop Must Slip
Exercise 13: Numerical Solution: Rolling WITH Slipping

THE HOP
Exercise 14: Airborne Hoop
Exercise 15: Time of Impact
Exercise 16: Putting It All Together

POSTSCRIPT: A FINAL SURPRISE

REFERENCES

NOTES TO THE INSTRUCTOR

SAMPLE SOLUTIONS TO EXERCISES

ABOUT THE AUTHORS