Rotational Motion

🟢 Lite — Quick Review (1h–1d)

Rapid summary for last-minute revision before your exam.

Rotational Motion — Key Facts Torque τ = r × F = rF sinθ (perpendicular component); SI unit: N·m = J Moment of Inertia I = Σmr²; depends on mass distribution and axis of rotation Angular momentum L = Iω = r × p; conservation when no external torque Rotational KE = ½Iω²; analogous to linear KE = ½mv² ⚡ Exam tip: For pure rolling (no slipping): v = ωr, a = αr, acm = αr

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🟡 Standard — Regular Study (2d–2mo)

Standard content for students with a few days to months.

Rotational Motion — NEET/JEE Study Guide Moment of inertia for common shapes: ring I = MR², disc I = MR²/2, solid sphere I = 2MR²/5, hollow sphere I = 2MR²/3, rod I = ML²/12 (about centre) Radius of gyration: k such that I = Mk²; physical meaning: all mass concentrated at distance k from axis Torque and angular acceleration: τ = Iα (Newton’s second law for rotation); α = τ/I Conservation of angular momentum: L = Iω = constant when τ_ext = 0; pirouette effect Angular impulse: equivalent to linear impulse but rotational; τΔt = ΔL

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🔴 Extended — Deep Study (3mo+)

Comprehensive coverage for students on a longer study timeline.

Rotational Motion — Comprehensive Notes Parallel axis theorem: I = I_cm + Md² (d = distance between parallel axes) Perpendicular axis theorem: I_z = I_x + I_y (for planar objects only, e.g. ring, disc) Precession: torque perpendicular to angular momentum → slow circular motion of axis; gyroscopes Kinetic energy of rolling: KE_total = ½mv_cm² + ½Iω² = ½(mv²)(1 + k²/r²); for ring k=r so KE_roll = mv² Dynamic equations: torque = Iα; power = τω; angular impulse = ΔL Work done in rotation: W = ∫τdθ; work-energy: W = Δ(½Iω²)

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