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Rotational Motion
Torque, moment of inertia, angular momentum
Key Concepts
- Torque (τ) is the rotational analogue of force
- Moment of inertia (I) depends on mass distribution and axis
- Angular momentum L = Iω is conserved when net torque = 0
- Rolling without slipping: v_cm = Rω
- Parallel axis theorem: I = I_cm + Md²
Important Formulae
| Torque | τ = Iα = r × F |
| Angular momentum | L = Iω |
| Rotational KE | KE = ½Iω² |
| I — solid sphere | I = 2/5 MR² |
| I — hollow sphere | I = 2/3 MR² |
| I — solid disk/cylinder | I = ½MR² |
| I — thin rod (centre) | I = ML²/12 |
Quick Tips
- A figure skater spins faster by pulling in arms — conservation of angular momentum (I decreases → ω increases).
- Total KE of rolling body = ½mv² + ½Iω² = ½mv²(1 + I/mR²).
- Perpendicular axis theorem (thin lamina): I_z = I_x + I_y.
Sample Practice Questions
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A hollow cylinder and solid cylinder of same mass and radius roll with same speed. Ratio of KE (hollow:solid):
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Answer: 4:3
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Torque = r × F. If r = 2 m and F = 10 N perpendicular, torque:
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Answer: 20 N·m
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Two equal masses are placed at ends of a rod of length L. Moment of inertia about midpoint:
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Answer: mL²/2
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Moment of inertia of a solid sphere about its diameter:
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Answer: 2MR²/5
Practice Questions
Practice 20 randomly selected NEET questions on Rotational Motion. Answers are revealed after each question.
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