The amount of force required to rotate a wheel depends on the torque and the radius of the wheel, not directly on its circumference. However, if we're considering the relationship in terms of how many times each wheel rotates when rolling the same distance, we can use the circumference to understand the relationship.
The larger wheel has triple the circumference of the smaller wheel. Therefore, for the same linear distance traveled, the larger wheel will make one-third the number of rotations as the smaller wheel. However, the question seems to be examining rotational dynamics rather than simple rolling distance.
If you're thinking about how much more input force or torque is needed to get the larger wheel rotating, the direct answer is somewhat complex and depends on many factors including radius, weight, and any resistances.
Therefore, without additional context, the answer would likely be:
one time
This assumes that we're considering a scenario where both wheels need to be rotated through the same angle, regardless of their size or circumferences. In practice, the total work done would depend on the radius and the inertia of the wheels.
2 answers