Chapter 3, Problem 3.16P

Consider the spur gears shown in Figure P3.15, where $I_1=0.1\text{ kg}\cdot {\text{m}}^2$ and $I_2=2\text{ kg}\cdot {\text{m}}^2$ . Shaft 1 rotates twice as fast as shaft 2. The torques are given as $T_1=10\text{N}\cdot \text{m}$ and $T_2=0$ . (a) Compute the angular acceleration ${\stackrel{\dot{}}{\omega }}_1$ . Assuming the shaft and gear inertias are negligible. (b) Suppose the gear on shaft 1 has an inertia $\text{0}\text{.005}\text{kg}\cdot {\text{m}}^2$ and the gear on shaft 2 has an inertia $\text{0}\text{.05}\text{kg}\cdot {\text{m}}^2$ . Compute the angular acceleration ${\stackrel{\dot{}}{\omega }}_1$ .