Answer
$v_B=10.2m/s$
$a_{Bt}=8m/s^2$
$a_{Bn}=258.66m/s^2$
Work Step by Step
The required velocity and acceleration can be determined as follows:
As $\omega^2=\omega_{\circ}^2+2\alpha (\theta-\theta_{\circ})$
$\implies \omega^2=(12)^2+2(20)[2(2\pi)-0]$
$\implies \omega=25.43rad/s$
We know that
$v_B=\omega r_B$
We plug in the known values to obtain:
$v_B=(25.43)(0.4)$
$\implies v_B=10.2m/s$
Now the tangential and normal components of acceleration are given as
$a_{Bt}=\alpha r_B$
We plug in the known values to obtain
$a_{Bt}=(20)(0.4)=8m/s^2$
Similarly, $a_{Bn}=\omega^2 r_B$
We plug in the known values to obtain:
$a_{Bn}=(25.43)^2(0.4)$
$\implies a_{Bn}=258.66m/s^2$
