Question

Hello I wanted to see if my answer matches yours:) please and thank you

Answer 1

SOLUTION:

Step 1:

In this question, we are given the following:

Step 2:

The details of the solution are as follows:

a) Given the diameter = 28 -inches

and Velocity = 55 mi/h

Then using the formula of angular speed, we have that:

$\begin{gathered} \text{v =}\omega\text{ r} \\ \text{Then,} \\ \text{v = }\omega(\frac{D}{2}) \\ \text{Then,} \\ w\text{ = }\frac{2v}{D} \\ But,\text{ } \\ v\text{ = 55 miles per hour to inches per minute = }58080\text{ inches per minute} \\ \text{D = 28 inches} \end{gathered}$

CONCLUSION OF PART A:

Now, we have that:

$\omega\text{ = }\frac{2\text{ x 58080}}{28}=\text{ 4148.571429 }\approx\text{ 4148. 6 rad/ min}$

PART B:

How many revolutions per minute do the wheel make? ( in rpm)

$\begin{gathered} 1Revolution\text{ = 2}\pi\text{ radians} \\ IRadian\text{ = }\frac{1}{2\pi}\text{ rev} \\ \text{Then,} \\ 4148.\text{ 6 rad/ min = 4148. 6 x }\frac{1}{2\pi}\text{ ( rev/ min)} \\ =\text{ 660. 3 rev/ min} \end{gathered}$

The wheel makes 660. 3 revolutions per minute.