(Solved): For the gear box shown, gears A, B, C, and D have radii of 15 mm,50mm,25mm, and 75mm, respect ...

For the gear box shown, gears A, B, C, and D have radii of 15 $\mathrm{mm},50\mathrm{mm},25\mathrm{mm}$, and $75\mathrm{mm}$, respectively. Shaft $D$ and $BC$ have moments of inertia of $0.025\mathrm{kg}?\mathrm{m}2$ and $0.01\mathrm{kg}?\mathrm{m}2$, respectively. A torque of $0.5\mathrm{N}?\mathrm{m}$ is applied to shaft $\mathrm{A}$ by a motor to overcome a load on the output shaft. You may ignore friction throughout as well as the inertia for shaft $A$. Also, you may assume the shafts are rigid. Find the value of a single equivalent inertia acting on shaft $D$ that represents the inertia of the whole system.