Answer
a) $a=2.2\frac{m}{s^2}$
$\alpha=6.9\frac{rad}{s^2}$
b) If the radius of tire is reduced to half, then angular acceleration will double.
Work Step by Step
(a) Linear acceleration is given as
$a=\frac{\Delta v}{\Delta t}$
We plug in the known values to obtain:
$a=\frac{45\frac{mi}{h}\times 0.447\frac{m}{s}/mi/h-0}{9.1}=2.2\frac{m}{s^2}$
Angular acceleration is given as
$\alpha=\frac{a}{r}$
$\implies \alpha=\frac{2.2}{0.32}=6.9\frac{rad}{s^2}$
(b) We know that angular acceleration and radius are inversely proportional, so if the radius of tire is reduced to half, then angular acceleration will double.
