Answer
(a) $d = 5.09~cm$
(b) $\alpha = 15.72~rad/s^2$
Work Step by Step
(a) The distance of one revolution is $\pi~d$, where $d$ is the diameter of the axle.
In one minute, the bucket moves $(2.00~cm/s)(60~s)$ which is 120 centimeters.
We can find the diameter $d$ of the axle.
$(7.5~rpm)(\pi~d) = 120~cm$
$d = \frac{120~cm}{(7.5~rpm)(\pi)}$
$d = 5.09~cm$
(b) $\alpha = \frac{a}{r} = \frac{0.400~m/s^2}{(\frac{0.0509~m}{2})}$
$\alpha = 15.72~rad/s^2$
