Question

The tires on your bicycle have a diameter of 20 inches. How many rotations does each tire make when you travel 500 feet? How many rotations does the tire make?

Answer 1

95.49 rotations

Explanation:

The circumference of each tire is given by πd, where d is the diameter of the tire. Therefore, the distance traveled by the tire after each full rotation is:

`C = \pi*d=\pi*20\\C= 62.832\ in`

The number of rotations by each tire after 500 feet (500 x 12 inches) is given by:

`n=(500*12)/(62.832)\\n=95.49\ rotations`

Each tire makes 95.49 rotations in 500 ft.

Answer 2

`\Delta n = 95.492\,rev`,
`\Delta \theta = 300\,rad`

Explanation:

The rotation measured in radians is:

`\Delta \theta = (\Delta s)/(r)`

`\Delta \theta = (500\,ft)/(\left((20)/(12)\,ft \right))`

`\Delta \theta = 300\,rad`

The number of revolutions is computed by simple rule of three:

`\Delta n = \left((300\,rad)/(\pi\,rad)\right) \cdot (1\,rev)`

`\Delta n = 95.492\,rev`