radius = 20 in. Linear speed = V = $15 \frac{miles}{hour}$
How many revolutions per minute is the wheel spinning?
W = angluar speed (in radians)
$V = rW$
$15 \frac{miles}{hour} = (20 in.)(W)$
How do you do the next step to solve for W ?
$$W = \frac{15 \frac{miles}{hour}}{20 in.}$$
Not sure the easiest way to simplify this.
If I convert 20 in. to .000315 miles, how is the result of dividing $15 \frac{mile}{hour}$ by .000315 miles ? Namely, what units are left when you divide $\frac{miles}{hour}$ by miles?
I ended up with:
$$W = \frac{15 \frac{miles}{hour}}{20 in.}=.75\frac{miles}{hour*in.}(\frac{1 hour}{60 mins})(\frac{1 rev}{2\pi rad})(\frac{12 in}{1 ft})(\frac{5280 ft}{1 mile}) = \frac{(.75)(12)(5280)}{(60)(2\pi)} \frac{revs}{mins}=126 \frac{revs}{mins}$$
I ended up with:
$$W = \frac{15 \frac{miles}{hour}}{20 in.}=.75\frac{miles}{hour*in.}(\frac{1 hour}{60 mins})(\frac{1 rev}{2\pi rad})(\frac{12 in}{1 ft})(\frac{5280 ft}{1 mile}) = \frac{(.75)(12)(5280)}{(60)(2\pi)} \frac{revs}{mins}=126 \frac{revs}{mins}$$