Answer
(a) The angular acceleration is $173~rad/s^2$
(b) The tangential acceleration is $2.16~m/s^2$
Work Step by Step
(a) We can express the angular displacement in units of radians:
$\Delta \theta = 15^{\circ}\times \frac{\pi~rad}{180^{\circ}} = 0.262~rad$
We can find the angular acceleration:
$\Delta \theta = \frac{1}{2}\alpha~t^2$
$\alpha = \frac{2\Delta \theta}{t^2}$
$\alpha = \frac{(2)(0.262~rad)}{(55\times 10^{-3}~s)^2}$
$\alpha = 173~rad/s^2$
The angular acceleration is $173~rad/s^2$
(b) We can find the tangential acceleration:
$a = \alpha~r$
$a = (173~rad/s^2)(0.0125~m)$
$a = 2.16~m/s^2$
The tangential acceleration is $2.16~m/s^2$
