Multiple Cholce Question The mass moment of inertia of a rotor is measured to be 211 b fts \( { }^{2} \) about its axis of rotation. Knowing that the kinetic friction causes a couple of magnitude 25 bet exerted on the rotor determine the rotor's deceleration. \( 0.0 .84 \mathrm{rad}^{2} \) \( 04.6 \mathrm{rad} \mathrm{s}^{2} \) \( 019260 \mathrm{rad}^{2} \) \( 01904 \mathrm{rad}^{2} \)

To determine the rotor's deceleration, we can use the relationship between torque (τ), moment of inertia (I), and angular acceleration (α), given by the equation: τ = I * α. The torque caused by the friction couple is 25 lb·ft. Rearranging the formula gives us α = τ / I. Plugging in the numbers, we have: α = 25 lb·ft / 211 lb·ft² = 0.118 rad/s². The negative sign indicates deceleration. To convert this to an equivalent radius of deceleration, we can conclude it is 0.118 rad/s². For context, this formula is essential in various engineering fields, including mechanical and aerospace engineering, where understanding the dynamics of rotating bodies, such as rotors or flywheels, is crucial for system design and performance analysis. As you ponder these concepts, remember that real-world applications include designing safer cars, enhancing performance in aircraft, and even improving efficient energy storage systems using flywheels!