Nathan,
You can test this for yourself. Get two balls, one big (like a
basketball) and one small (like a tennis ball). Roll them side by side
across the floor with the same speed. You will see that even though the
balls have the same speed, the small ball is turning faster. In other
words, the small ball will make more turns when rolling a fixed
distance that the big ball will when rolling the same distance.
This is easy to understand. The small ball, just like a small
wheel, will move a shorter distance every time it makes one turn than
the big one does, so the small one has to make more turns.
It's a bit like a small kid walking next to her dad. Every step she
takes moves her a shorter distance that every step the father takes, so
the kid has to take more steps to walk the same distance. This means
the kid has to take quicker steps to keep up, just like a smaller wheel
has to make more turns to keep up to a bigger one.
Mats
(published on 10/22/2007)
