Rotational Motion Revision Notes for NEET Physics PDF Download
🌀 ROTATIONAL MOTION · Rigid Body Dynamics
Moment of Inertia • Torque • Angular Momentum • Rolling Motion • NEET problems
📐 ROTATIONAL KINEMATICS
Analogous to linear motion with θ (angular displacement), ω (angular velocity), α (angular acceleration).
ω = dθ/dt, α = dω/dt
Equations for constant α:
ω = ω₀ + αt
θ = ω₀t + ½αt²
ω² = ω₀² + 2αθ
Relation between linear & angular:
v = rω, at = rα, ac = rω²
⚙️ MOMENT OF INERTIA (I)
Rotational analogue of mass. I = Σ mi ri² (for discrete), I = ∫ r² dm (continuous).
📌 Common MIs (about axis through CM)
- Rod (length L): ICM = ML²/12
- Ring: I = MR²
- Disc: I = ½ MR²
- Solid sphere: I = ⅖ MR²
- Hollow sphere: I = ⅔ MR²
🔧 Theorems
Parallel axis: I = ICM + Md²
Perpendicular axis (for lamina): Iz = Ix + Iy
✏️ MI of a rod about CM & end
🔧 TORQUE (τ) & ROTATIONAL DYNAMICS
Torque = r × F → magnitude: τ = rF sinθ. τ = I α (Newton's 2nd law for rotation).
For a system of particles, net external torque = dL/dt.
Work-energy: Wrot = ∫ τ dθ = ΔKrot = ½ I ω² – ½ I ω₀².
🌀 ANGULAR MOMENTUM (L)
L = Iω (for rigid body about fixed axis). Direction: along axis (right-hand rule).
For a particle: L = r × p = m(r × v).
💫 Conservation: Li = Lf
⚡ ROLLING MOTION (Pure Rolling)
Combination of translation + rotation. Condition: vCM = Rω (no slipping).
Total KE = ½ M vcm² + ½ Icm ω² = ½ M vcm² (1 + k²/R²) where k = radius of gyration.
Acceleration on incline: a = g sinθ / (1 + I/MR²). For disc: a = (2/3)g sinθ; for ring: a = (1/2)g sinθ.
🖍️ Pure rolling on incline
💡 NEET TIPS & SHORTCUTS
- For rolling objects, the one with smallest I/MR² (disc, sphere) reaches bottom first on incline.
- In conservation of L, if moment of inertia changes, angular velocity changes inversely.
- Torque = rate of change of angular momentum; if torque is zero, L constant.
- Use parallel axis theorem to find I about any axis quickly.
⚠️ COMMON MISTAKES
- Using I = MR² for all bodies – memorize standard MIs.
- Forgetting direction in torque (use sign convention).
- Assuming friction always opposes motion – in pure rolling, static friction may act up or down incline.
- Applying conservation of angular momentum when external torque acts.
📌 QUICK REVISION CARD
Rotational KE: Krot = ½ Iω²
Torque: τ = Iα = r × F
Angular momentum: L = Iω
Rolling KE: K = ½ Mv² (1 + I/MR²)
Parallel axis: I = ICM + Md²
Perpendicular axis (lamina): Iz = Ix + Iy