Answer
The net external torque acting on the hoop wheel is $0.2N.m$ and the one acting on the disk wheel is $0.1N.m$
Work Step by Step
1) Find the angular acceleration of the each wheel
We have $\omega_0=0$, $\theta=13rad$ and $t=8s$. We have, $$\theta=\omega_0t+\frac{1}{2}\alpha t^2=\frac{1}{2}\alpha t^2$$ $$\alpha=\frac{2\theta}{t^2}=0.41rad/s^2$$
2) The net torque acting on the each wheel is $$\sum\tau=I\alpha$$
From Table 9.1, the hoop wheel has $I_1=mr^2=4(0.35)^2=0.49kg.m^2$
$$\sum\tau_1=I_1\alpha=0.2N.m$$
From Table 9.1, the solid disk wheel has $I_2=1/2mr^2=0.245kg.m^2$
$$\sum\tau_2=I_2\alpha=0.1N.m$$
