Rotational Motion – Stage 1 (Page 11)

Complete Review (Page 1 → Page 10)

This page summarizes the entire Stage-1 of Rotational Motion. It is designed to help students revise concepts quickly and understand how all ideas are connected.

                                                    

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1. Basics of Rotational Motion (Page 1)

✔ Rotation about a fixed axis
✔ Angular displacement (θ), angular velocity (ω), angular acceleration (α)
✔ Units and basic definitions

Key idea: Rotation is motion in a circular path about an axis.

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2. Angular Kinematics (Page 2)

✔ Equations of angular motion
✔ Relation between linear and angular quantities
✔ v = rω, a_t = rα, a_c = rω²

These relations connect rotational motion with linear motion.

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3. Torque (Page 3)

✔ Turning effect of force
✔ τ = r × F = rF sinθ
✔ Moment arm concept

Torque decides whether a force can rotate a body.

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4. Angular Momentum & Equilibrium (Page 4)

✔ L = r × p
✔ τ = dL/dt
✔ Conservation of angular momentum
✔ Rotational equilibrium (Στ = 0)

This section explains why spinning systems behave differently.

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5. Moment of Inertia (Page 5)

✔ I = mr² (particle)
✔ I = Σmᵢrᵢ² (system)
✔ Rotational analogue of mass

Moment of inertia controls how easily a body rotates.

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6. Radius of Gyration & Standard M.I. (Page 6)

✔ I = Mk²
✔ Standard M.I. of rod, disc, ring, sphere
✔ Importance of axis

Memorizing standard M.I. values saves exam time.

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7. Axis Theorems (Page 7)

✔ Parallel axis theorem: I = I_cm + Md²
✔ Perpendicular axis theorem: I_z = I_x + I_y

These theorems simplify complicated M.I. calculations.

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8. Rotational Energy & Work (Page 8)

✔ K_rot = ½ Iω²
✔ Total KE in rolling
✔ Work–energy theorem for rotation

Energy methods are powerful in solving tough problems.

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9. Rotational Dynamics (Page 9)

✔ τ = Iα
✔ Rotational form of Newton’s second law
✔ Importance of net torque

This equation governs rotational acceleration.

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10. Rolling Motion (Page 10)

✔ Combination of translation and rotation
✔ No-slipping condition: v = ωR
✔ Acceleration on incline depends on M.I.
✔ Role of friction

Rolling motion is the most tested application in IIT/JEE.

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Final Exam Insight

Rotational motion is not about memorizing formulas. It is about choosing the correct axis, identifying forces and torques, and applying the right method (force or energy).

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Stage 1 COMPLETED ✅
Next: Stage 2 – Board Exam Questions (Short & Long)