If you have a 40 inch wheel connected to a 20 inch wheel connected to a 5 inch wheel how many rotations need to make in order for the 40inch wheel to make 1rotation?
To determine how many rotations the smaller wheels need to make in order for the larger wheel (40-inch wheel) to make one full rotation, you need to consider the concept of gear ratios.
In this case, the gear ratio can be determined by comparing the circumferences of the wheels. The circumference of a circle is calculated by multiplying its diameter by π (pi), which is approximately 3.14159.
Given wheel diameters:
- 40-inch wheel: Diameter = 40 inches
- 20-inch wheel: Diameter = 20 inches
- 5-inch wheel: Diameter = 5 inches
Now, let's calculate the circumferences:
- Circumference of 40-inch wheel = π * 40 = 3.14159 * 40 ≈ 125.66368 inches
- Circumference of 20-inch wheel = π * 20 = 3.14159 * 20 ≈ 62.83184 inches
- Circumference of 5-inch wheel = π * 5 = 3.14159 * 5 ≈ 15.70795 inches
To find the gear ratio between the 40-inch wheel and the 5-inch wheel, you need to compare their circumferences:
- Gear ratio = Circumference of 40-inch wheel / Circumference of 5-inch wheel
= 125.66368 inches / 15.70795 inches
≈ 8
Thus, the gear ratio between the 40-inch wheel and the 5-inch wheel is approximately 8. This means that for every 8 rotations of the smaller (5-inch) wheel, the larger (40-inch) wheel will make one full rotation.
Therefore, in order for the 40-inch wheel to make one full rotation, the 5-inch wheel needs to make 8 rotations.