Rotational Kinetic Energy
A disc with moment of inertia 0.5 kg·m² rotates about its central axis at an angular velocity of 4 rad/s. What is the rotational kinetic energy stored in the rotating disc?
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About This Question
- Subject
- physics
- Chapter
- rotational motion
- Topic
- rotational kinetic energy
- Difficulty
- Easy
- Year
- 2025
Solution
Correct Answer:
4 J
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.
This easy difficulty physics question is from the chapter rotational motion, covering the topic of rotational kinetic energy. It appeared in the 2025 exam.
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