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

Answer:

95.49 rotations

Step-by-step 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:

$n=\frac{500*12}{62.832}\\n=95.49\ rotations$

Each tire makes 95.49 rotations in 500 ft.

Answer 2

Answer:

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

Step-by-step explanation:

The rotation measured in radians is:

$\Delta \theta = \frac{\Delta s}{r}$

$\Delta \theta = \frac{500\,ft}{\left(\frac{20}{12}\,ft \right)}$

$\Delta \theta = 300\,rad$

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

$\Delta n = \left(\frac{300\,rad}{\pi\,rad}\right) \cdot (1\,rev)$

$\Delta n = 95.492\,rev$