College Physics (4th Edition)

(a) The angular acceleration is $173~rad/s^2$ (b) The tangential acceleration is $2.16~m/s^2$
(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 $2.16~m/s^2$