Rotational Kinetic Energy

Per NCERT Class 11, Chapter 7 (System of Particles and Rotational Motion), a rotating rigid body stores kinetic energy given by KE = ½Iω², which is the exact rotational counterpart of the linear expression ½mv². In this analogy the moment of inertia I plays the role of mass and the angular velocity ω replaces the linear speed v, so a body resists changes to its spin in the same way a massive object resists changes to its linear motion. Substituting the data for the disc: KE = ½ × 0.5 × (4)² = ½ × 0.5 × 16 = 0.25 × 16 = 4 J. The option 8 J results from omitting the factor of ½ and is therefore exactly double the correct value. The option 2 J comes from using ω instead of ω², losing the essential square on the angular velocity. The option 16 J keeps only the ω² term and ignores both the factor of ½ and the moment of inertia. A plausibility check confirms the units: kg·m² times (rad/s)² reduces to joules because the radian is dimensionless, and 4 J is a sensible amount of energy for a small disc spinning at 4 rad/s.