Final answer:
A big wheel with twice the circumference of a small wheel will rotate with half the force and twice the speed of the small wheel.
Step-by-step explanation:
A big wheel with twice the circumference of a small wheel will rotate with half the force and twice the speed of the small wheel.
This is because the force required to rotate an object is directly proportional to its radius. A larger wheel will have a larger radius, thus requiring more force to rotate it. On the other hand, the speed at which an object rotates is inversely proportional to its radius. A larger wheel will have a larger radius, resulting in a slower rotational speed.
For example, let's say the small wheel has a circumference of 10 cm. The big wheel will have a circumference of 20 cm (twice as large). If the small wheel rotates with a force of 10 N and a speed of 5 rad/s, the big wheel will rotate with a force of 5 N (half the force) and a speed of 10 rad/s (twice the speed).