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| UNIT: | Rolling of rigid hoops, cylinders and spheres | |||||||||
| PURPOSE: | Develop an intuition for the concept of moment of inertia and for its role in rolling motion | |||||||||
| EQUIPMENT: |
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| SUGGESTIONS: | Set up races and ask for predictions of results:
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| DISCUSSION: | Let g
be the shape factor (g=1 for cyl. shell, g=2/3
for sph. shell, g=1/2 for cylinder, g=2/5 for sphere). Then kinetic energy
of rolling (without slipping) is KE=Mv2(1+g)/2 where v is the center of
mass speed. Thus objects with the smaller g win the race, independently
of M.
A box with numerous objects for rolling is provided. Some of the possible races are illustrated below. There are also a number of "trick" objects. |
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1. Equipment and set-up
2. Two solid balls of different radius before being released
(a wooden block is used as a starting gate each time)
3. Two balls in #2 rolling down
4. Two solid cylinders of different lengths and same radius
rolling down
5. Two hollow cylinders of different lengths and same radius
rolling down
6. Two hollow cylinders of same lengths and different radii
rolling down
7. A hollow and a solid cylinder of the same radius rolling
down
8. A ball and a solid cylinder rolling down
9. A solid and a hollow ball rolling down