The Strange Behavior of Rolling Things 
The Strange Behavior of Rolling Things
by Prof. Miller
Video Lecture 12 of 46
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Date Added: February 5, 2015

Lecture Description

When we roll things down an inclined plane we discover a strange business: The mass of the rolling body does not matter. What matters is how the mass is distributed. To explore these wonderful thing we roll disks and hoops and spheres - all sizes - all masses and very enchanting discoveries are made.

A - We first roll a solid disk and a hoop. They have the same diameter -
the same mass - the same weight. How do they roll? That is - do they roll together? Does the disk win? Does the hoop win? We discover that the disk beats the hoop.

B - Now we roll an array of disks and hoops. And what do we find? We find that ALL disks roll alike. We find that ALL hoops roll alike. AND - we find that every disk beats every hoop. Little disks - big disks - fat disks - skinny disks - ALL DISKS BEAT ALL HOOPS. Now -how can I say this? One cannot roll ALL the disks and all the hoops in the whole WoTId! ANSWER: The MATHEMATICS tells us all this in a jiffy:
FR = lot and Mgh = 1/2 MV + 1/2 \(n . So you see how very much a brief sentence in mathematics can tell us.

C - We further find that ALL SPHERES ROLL ALIKE. Little spheres - big spheres - tiny spheres - ALL SPHERES - roll alike. But they must be solid uniform spheres like steel balls.

D - Now the question: Suppose we roll disks and spheres and hoops? What now? And to sum up our wonderful discoveries we say:
1 - All disks roll alike
2 - All hoops roll alike
3 - All spheres roll alike
4 - All spheres beat all disks
5 - All disks beat all hoops.
This is really wonderful to know.

E - The bodies we have rolled are very special. They are uniform in their mass distribution. So - we ask: what happens if the bodies are "loaded"? And so we roll two disks - one loaded near the center - one loaded at the edge. The centrally-loaded one wins.

F - The Yo-Yo has interesting behavior. It is a disk with an axis and the cis* rolls down a string. The string is like an inclined plane which is vertical. The mathematics above tells us how it rolls.

G - If a wheel - a disk - a ring - rolls without slipping on a roadway a good question to ask is this: What is the path marked out - traced out -described - by a point on the edge of the rolling wheel? The answer is very dramatic. The curve is called a cycloid and it is a very pretty thing to study.

Course Index

  1. The Idea of the Center of Gravity
  2. Newton's First Law of Motion: Inertia
  3. Newton's Second Law of Motion: The Elevator Problem
  4. Newton's Third Law of Motion: Momentum
  5. Energy and Momentum
  6. Concerning Falling Bodies & Projectiles
  7. The Simple Pendulum and Other Oscillating Things
  8. Adventures with Bernoulli: Bernoulli's Principle
  9. Soap Bubbles and Soap Films
  10. Atmospheric Pressure
  11. Centrifugal Force and Other Strange Matters
  12. The Strange Behavior of Rolling Things
  13. Archimedes' Principle
  14. Pascal's Principle: The Properties of Liquids
  15. Levers, Inclines Planes, Geared-wheels and Other Machines
  16. The Ideas of Heat and Temperature
  17. Thermometric Properties and Processes
  18. How to Produce Heat Energy
  19. Thermal Expansion of Stuff: Solids
  20. Thermal Expansion of Stuff: Gases & Liquids
  21. The Strange Thermal Behavior of Ice and Water
  22. Heat Energy Transfer by Conduction
  23. Heat Energy Transfer by Convection
  24. Heat Energy Transfer by Radiation
  25. Evaporation, Boiling, Freezing: A Dramatic Adventure
  26. Miscellaneous Adventures in Heat
  27. The Drama in Real Cold Stuff: Liquid Nitrogen
  28. The Physics of Toys: Mechanical
  29. The Physics of Toys: Acoustic and Thermal
  30. Waves: Kinds of Properties
  31. Sound Waves: Sources of Sound & Pitch and Frequency
  32. Vibrating Bars and Strings: The Phenomenon of Beats
  33. Resonance: Forced Vibrations
  34. Sounding Pipes
  35. Vibrating Rods and Plates
  36. Miscellaneous Adventures in Sound
  37. Electrostatic Phenomena: Foundations of Electricity
  38. Electrostatic Toys, Part 1
  39. Electrostatic Toys, Part 2
  40. Adventures with Electric Charges
  41. Adventures in Magnetism
  42. Ways to "Produce" Electricity
  43. Properties and Effects of Electric Currents
  44. Adventures in Electromagnetism
  45. Further Adventures in Electromagnetism
  46. Miscellaneous and Wondrous Things in E&M

Course Description

Demonstrations in Physics was an educational science series produced in Australia by ABC Television in 1969. The series was hosted by American scientist Julius Sumner Miller, who demonstrated experiments involving various disciplines in the world of physics. The series was also released in the United States under the title Science Demonstrations.

This program was a series of 45 shows (approximately 15 minutes each) on various topics in physics, organized into 3 units: Mechanics; Heat and Temperature / Toys; and Waves and Sound / Electricity and Magnetism.

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