Question

A wheel on a tractor has a circumference of 48(pi) inches. If the wheel is turning at a rate of 1.5 revolutions per second, find the linear speed of the wheel in miles per hour. Round answer to the nearest tenth.

Answer 1

Given,

The circumference of the wheel is L=48 (pi).

The rate of revolution is

$\omega=\frac{1.5rev}{\sec }$

Let the radius be r.

Thus,

$2\pi r=48\pi$$\Rightarrow r=24\text{ inch}$

Thus the linear speed is:

$v=r\omega=24inch\times\frac{1.5rev}{s}=24\times0.025\times3\pi\text{ m/s}$

Thus,

$v=5.7453\times\frac{3600}{1609}=12.9\text{ mile/hr}$

The answer is :

The linear speed of the wheel is 12.9 miles per hour