1. **Problem 1: Determine the RPM of gear 2** given gear 1 has 100 teeth, rotates at 1180 rpm, and gear 2 has 500 teeth. 2. The formula relating gear teeth and RPM is $$T_1 \times N_1 = T_2 \times N_2$$ where $T$ is teeth count and $N$ is RPM. 3. Rearranging to find $N_2$: $$N_2 = \frac{T_1 \times N_1}{T_2}$$ 4. Substitute values: $$N_2 = \frac{100 \times 1180}{500}$$ 5. Simplify: $$N_2 = \frac{\cancel{100} \times 1180}{\cancel{500}} = \frac{100 \times 1180}{500} = 236$$ rpm 6. **Answer for Problem 1:** Gear 2 rotates at 236 rpm. 1. **Problem 2: Determine the Torque on gear 2** given gear 1 has 100 teeth, rotates at 1970 rpm with torque 2137 Nm, and gear 2 has 500 teeth. 2. The torque and teeth relationship is $$T_1 \times N_1 = T_2 \times N_2$$ and torque is inversely proportional to speed, so torque on gear 2 is $$\tau_2 = \tau_1 \times \frac{T_2}{T_1}$$ 3. Substitute values: $$\tau_2 = 2137 \times \frac{500}{100}$$ 4. Simplify: $$\tau_2 = 2137 \times 5 = 10685$$ Nm 5. **Answer for Problem 2:** Torque on gear 2 is 10685 Nm.