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Sagot :
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:
[tex]\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}[/tex]CONCLUSION OF PART A:
Now, we have that:
[tex]\omega\text{ = }\frac{2\text{ x 58080}}{28}=\text{ 4148.571429 }\approx\text{ 4148. 6 rad/ min}[/tex]PART B:
How many revolutions per minute do the wheel make? ( in rpm)
[tex]\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}[/tex]The wheel makes 660. 3 revolutions per minute.
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