- #1

**Wheel size and speed help!**

Okay, my father and I have been an argument for days on this. We were arguing about wheel sizes and their effected distance traveled. A larger wheel has a greater circumference; therefore one revolution will travel a farther distance. Here's the argument. If you have two wheels of different sizes, one small and one large, and rotate them with the exact same force on an axle- Will the larger wheel travel a farther distance in a given time because it can cover more distance, or because it actually rotates faster at the point of contact on the ground. My argument is the smaller wheel and the larger wheel can actually be "spinning" (rotational speed) at the exact same speed, but because a larger wheel will cover a greater distance on one complete turn, will move faster along a plain. I understand that if they spin the same speed, the smaller wheel will have made a complete turn before the larger wheel. It is my belief that even though this is true, the larger wheel has still made enough distance (even though it has not yet made a complete revolution) to eventually cover more ground; thus, creating more distance; thus having a faster linear speed. So I guess after all that mumbo jumbo, I'm trying to ask do two wheels of different sizes travel at different linear speeds with the same rotational speed at the axle because of size, or because of the speed of the two wheels (at the point of contact on the ground) actually changes (rule out all variables: surface friction, wind, etc.)? I hope someone can make sense of all of this and put a stop to our bickering :).

P.S. Also, If I took two wheels, again of different sizes- one large, one small, and started them on top of a slope. If I let go of both wheels at the same time (these wheels are the same weight) would the larger wheel reach the end before the smaller wheel? Or would they reach at the same time? Also, let's say that the slope was long enough for each wheel to reach maximum speed. Please explain the answer to this.