Me graw Exit Assignment 2 of 12 Concepts completed Multiple Cholce Questlon A rotor rotating about a fixed axis through its mass center has a mass of 50 kg , radius of gyration of 50 mm , and angular acceleration of 11 rad \( / \mathrm{s}^{2} \). Determine the moment about its fixed axis. 2.2 kNm 1.375 Nm 0.0113 Nm 27.5 Nm

To calculate the moment (torque) about the fixed axis for the rotor, you can use the formula: \[ \text{Moment} = I \cdot \alpha \] where \( I \) is the moment of inertia and \( \alpha \) is the angular acceleration. The moment of inertia \( I \) can be calculated using the formula: \[ I = m \cdot k^2 \] Here, \( m = 50 \, \text{kg} \) and \( k = 0.05 \, \text{m} \) (since 50 mm is 0.05 m). Plugging in the values: \[ I = 50 \, \text{kg} \cdot (0.05 \, \text{m})^2 = 50 \cdot 0.0025 = 0.125 \, \text{kg} \cdot \text{m}^2 \] Now, substitute \( I \) and \( \alpha = 11 \, \text{rad/s}^2 \) into the moment formula: \[ \text{Moment} = 0.125 \, \text{kg} \cdot \text{m}^2 \cdot 11 \, \text{rad/s}^2 = 1.375 \, \text{Nm} \] Thus, the correct answer is **1.375 Nm**. Remember, in problems like these, always break it down step by step and double-check your unit conversions to avoid slip-ups! Also, consider keeping a calculator handy and practicing similar problems to get the hang of the concepts.