Answer:
Approximately [tex]\rm 1.15\; m \cdot s^{-1}[/tex].
Explanation:
The equation in the hint [tex]v = r \cdot \omega[/tex] relates the linear speed [tex]v[/tex] of an object to its angular speed [tex]\omega[/tex]and its radius [tex]r[/tex].
Both [tex]\omega[/tex] and [tex]r[/tex] are given. However, [tex]\omega[/tex] is in the non-standard unit of (RPM) rotations per minutes. To make sure that this equation gives the linear velocity in its standard SI unit [tex]\rm m \cdot s^{-1}[/tex], convert [tex]\omega[/tex] to the its standard unit radians-per-second.
The wheel rotates [tex]44[/tex] times each minute. Divide that by [tex]60[/tex] (number of seconds in each minute) to get the number of rotations in each second. The wheel turns [tex]11/15[/tex] of a rotation in each second on average.
The angular distance in each rotation is [tex]2\pi[/tex] radians. Multiply the number of rotations in each second by [tex]2\pi[/tex] to get the number of radians in each second. The angular velocity [tex]\omega[/tex] of the wheel is [tex]1.15[/tex] radians per second.
Convert the radius of the circle to standard units: [tex]r = \rm 25.0\; cm = 0.250 \; m[/tex].
Apply the equation. Note that the "radians" part of the unit "radians per second" is ignored in this calculation.
[tex]v = r \cdot \omega = \rm 0.250\; m \cdot 1.15\; s^{-1} \approx 1.15\; m \cdot s^{-1}[/tex].
