Answer
When $R_1 = 0.025~m$, then $f = 480~rpm$
When $R_2 = 0.058~m$, then $f = 210~rpm$
Work Step by Step
We can use the speed $v$ to find $\omega$.
$\omega = \frac{v}{R}~rad/s$
We can use $\omega$ to find the frequency $f$ in rpm:
$f = (\frac{\omega~rad/s}{2\pi~rad/rev})(\frac{60~s}{1~min})$
$f = (\frac{60~v}{2\pi~R})~rpm = (\frac{30~v}{\pi~R})~rpm$
We can find $f$ when $R_1 = 0.025~m$:
$f = (\frac{30~v}{\pi~R})~rpm = (\frac{(30)(1.25)}{0.025~\pi})~rpm = 480~rpm$
When $R_1 = 0.025~m$, then $f = 480~rpm$.
Next, we find $f$ when $R_2 = 0.058~m$:
$f = (\frac{30~v}{\pi~R})~rpm = (\frac{(30)(1.25)}{0.058~\pi})~rpm = 210~rpm$
When $R_2 = 0.058~m$, then $f = 210~rpm$.
