Rotational Kinematics

Following NCERT Class 11, Chapter 7 (System of Particles and Rotational Motion), rotational kinematics mirrors linear kinematics, with the equation ω = ω₀ + αt linking the final angular velocity, the initial angular velocity, the angular acceleration, and the elapsed time. These equations are valid only when the angular acceleration is constant, which the problem explicitly states for the flywheel. The angular acceleration α is itself the rate of change of angular velocity, just as linear acceleration is the rate of change of linear velocity. Here ω₀ = 0 because the flywheel starts from rest, ω = 60 rad/s, and t = 12 s. Rearranging the equation gives α = (ω - ω₀)/t = (60 - 0)/12 = 5 rad/s². The option 0.2 rad/s² results from inverting the ratio and dividing time by velocity instead. The option 720 rad/s² comes from multiplying the two quantities rather than dividing. The option 12 rad/s² mistakenly repeats the time value with no calculation. A units check confirms rad/s² is the correct unit for angular acceleration, and the magnitude of 5 rad/s² is entirely reasonable for a flywheel that smoothly reaches 60 rad/s over a span of 12 seconds.