Torque And Angular Acceleration

NCERT Class 11, Chapter 7 (System of Particles and Rotational Motion) establishes the rotational form of Newton's second law, τ = Iα, where the net torque equals the product of the moment of inertia and the angular acceleration. This is the direct angular counterpart of the linear law F = ma, with torque taking the place of force and moment of inertia taking the place of mass. The equation tells us that for a given torque, a body with a larger moment of inertia is harder to angularly accelerate, just as a heavier object is harder to push. Rearranging for the angular acceleration gives α = τ/I = 10/2 = 5 rad/s². The option 20 rad/s² comes from multiplying torque by inertia instead of dividing. The option 0.2 rad/s² inverts the ratio by dividing inertia by torque. The option 12 rad/s² bears no valid relationship to the given quantities. A check of units shows that N·m divided by kg·m² yields s⁻², which corresponds to rad/s² since the radian is dimensionless, confirming the dimensional consistency. A value of 5 rad/s² is physically reasonable for a moderately heavy grinding wheel subjected to a steady 10 N·m torque about its axis.