Pessimist Singularitarian

#5
November 25th, 2016,
23:10
Let's begin by taking the formula Dan provided, and solve for $r$:

$ \displaystyle r=\frac{v}{\omega}$

Now, we know the radius $r$ is half the diameter $d$:

$ \displaystyle d=\frac{2v}{\omega}$

We are given:

$ \displaystyle v=19\text{ mph}\cdot\frac{5280\text{ ft}}{1\text{ mi}}\cdot\frac{1\text{ hr}}{60\text{ min}}=1672\,\frac{\text{ft}}{\text{min}}$

Now we need to turn 10 revolutions per minutes into an angular velocity given in radians (dimensionless) per minute:

$ \displaystyle \omega=10\,\frac{\text{rev}}{\text{min}}\cdot\frac{2\pi}{1\text{ rev}}=20\pi\,\frac{1}{\text{min}}$

So, plug in these values...what do you get for $d$?