One revolution corresponds to an angular displacement of [tex]2\pi[/tex], so its angular speed is
[tex]32\,\mathrm{rpm}=\left(32\dfrac{\rm rev}{\rm min}\right)\left(2\pi\dfrac{\rm rad}{\rm rev}\right)=64\pi\dfrac{\rm rad}{\rm min}[/tex]
[tex]\pi[/tex] radians is equivalent to 180 degrees, so the angular speed could also be
[tex]\left(64\pi\dfrac{\rm rad}{\rm min}\right)\left(\dfrac{180}\pi\dfrac{\rm deg}{\rm rad}\right)=11,520\dfrac{\rm deg}{\rm min}[/tex]
The linear speed depends on the wheel's radius. Suppose its radius is [tex]r[/tex]. Then the wheel has circumference [tex]2\pi r[/tex] units. A point on the edge of the wheel travels this distance in one revolution, so its linear speed is
[tex]\left(32\dfrac{\rm rev}{\rm min}\right)\left(2\pi r\dfrac{\rm u}{\rm rev}\right)=64\pi r\dfrac{\rm u}{\rm min}[/tex]
(where [tex]u[/tex] stands for units of length)
