When we are converting units, whether in math or science, using dimensional analysis is both easy and reliable. What we will do is simply multiply by conversion fractions = 1 until we have the units we want:
For this example, we also want to note that 26-inch diameter wheels have circumference = 26π inches.
(60 mi / 1 hr )⋅(1 hr / 60 min)⋅(5,280 ft / 1 mi)⋅(12 in / 1 ft)⋅(1 revolution / 26π in)⋅( 2π rads / 1 revolution) ~
4,874 rads / min. Notice how the units cancel out to give us the units we want.
Btw, multiplying by the last 2 fractions above is equivalent to dividing by the radius, which is how angular speed and linear speed are related in physics: ν = ωr. This also reflects arc length formula s = rθ, for θ in rads.
