Example 1 · level 1
A solid disc of mass 4 kg and radius 1 m spins about its central axis (I = ½MR²) at 2 rad/s. Find its rotational kinetic energy (in J, correct to 2 decimal places).
Show solution
- I = 2 kg m².
- KE = ½ × I × 2² = 4 J.
Answer: 4 J
CLASS 11–12 PHYSICS · SYSTEM OF PARTICLES AND ROTATIONAL MOTION
Moment of inertia and rotational kinetic energy
Rotational KE = ½Iω². Ring: I = MR²; disc: ½MR²; solid sphere: (2/5)MR²; hollow sphere: (2/3)MR². Rolling without slipping: KE = ½Mv²(1 + I/MR²).
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Worked examples
Example 2 · level 2
A ring of mass 4 kg rolls without slipping at 2 m/s on a level floor. Find its total kinetic energy (in J, correct to 2 decimal places).
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- Translational = 8 J.
- Rotational = 8 J.
- Total = 16 J.
Answer: 16 J
Example 3 · level 3
A hollow sphere rolls without slipping. What fraction of its total kinetic energy is rotational? (Give a fraction.)
Show solution
- Fraction = k/(1 + k) = 2/5.
Answer: 2/5