Answer
$\alpha = 5.6~rad/s^2$
Work Step by Step
We can find the angular speed when $v = 12~m/s$:
$\omega_0 = \frac{v}{r}$
$\omega_0 = \frac{12~m/s}{0.375~m}$
$\omega_0 = 32~rad/s$
We can find the angular speed when $v = 25~m/s$:
$\omega_f = \frac{v}{r}$
$\omega_f = \frac{25~m/s}{0.375~m}$
$\omega_f = 66.67~rad/s$
We can find the average angular acceleration:
$\omega_f = \omega_0+\alpha~t$
$\alpha = \frac{\omega_f - \omega_0}{t}$
$\alpha = \frac{66.67~rad/s - 32~rad/s}{6.2~s}$
$\alpha = 5.6~rad/s^2$
