Question

# A wheel is rolling with a speed of 9.55 miles per hour. How many revolutions per minute is the wheel completing if its diameter is 8.5ft?

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A wheel is rolling with a speed of 9.55 miles per hour. How many revolutions per minute is the wheel completing if its diameter is 8.5ft?

2021-03-05

The formula:
$$v=rw$$
First, convert to ft/min:
$$\displaystyle{v}=\frac{{{9.55}{m}{i}}}{{{h}{r}}}\times\frac{{{5280}{f}{t}}}{{{1}{m}{i}}}\times\frac{{{1}{h}{r}}}{{{60}\min}}={840.4}$$ ft per min
Substitute $$\displaystyle{r}=\frac{{d}}{{2}}{\quad\text{and}\quad}{v}={840.4}:$$
$$\displaystyle{840.4}={\left(\frac{{8.5}}{{2}}\right)}{w}$$
$$\displaystyle{w}=\frac{{840.2}}{{4.25}}$$ rad per min
Convert to rev per min:
$$\displaystyle{w}=\frac{{840.2}}{{4.25}}\times\frac{{1}}{{{2}\pi}}$$
$$\displaystyle{w}\approx{31.5}$$ rev per min