## Physics for Scientists and Engineers: A Strategic Approach with Modern Physics (4th Edition)

(a) $\alpha = 4.0~rad/s^2$ (b) $a_t = 0.12~m/s^2$
(a) $\omega = (2.0+\frac{1}{2}t^2)~rad/s$ $\alpha = \frac{d\omega}{dt}$ $\alpha = (t)~rad/s^2$ We can find the angular acceleration at t = 4.0 s: $\alpha = (t)~rad/s^2$ $\alpha = 4.0~rad/s^2$ (b) We can find the tangential acceleration $a_t$ of a tooth on the gear. $a_t = \alpha ~r$ $a_t = (4.0~rad/s^2)(0.030~m)$ $a_t = 0.12~m/s^2$