Chapter 16 - Planar Kinematics of a Rigid Body - Section 16.3 - Rotation about a Fixed Axis - Problems - Page 331: 3

$v_A=26m/s$ $a_{At}=10m/s^2$ $a_{An}=1352m/s^2$

We know that $\omega=\omega_{\circ}+\alpha t$ We plug in the known values to obtain: $\omega=12+20(2)$ $\omega=52rad/s$ Now, $v_A=\omega r_A$ We plug in the known values to obtain: $v_A=(52)(0.5)$ $\implies v_A=26m/s$ The tangential and normal components of acceleration are given as $a_{At}=\alpha r_A$ $\implies a_{At}=\alpha r_A$ We plug in the known values to obtain: $a_{At}=(20)(0.5)=10m/s^2$ Similarly, $a_{An}=\omega^2 r_A$ We plug in the known values to obtain: $a_{An}=(52)^2(0.5)$ $\implies a_{An}=1352m/s^2$