# THE ULTIMATE PHYSICS CHEAT SHEET: ROTATIONAL MOTION
(Advanced Placement & International Curriculum)
1. KINEMATICS COMPARISON
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- Displacement: s = r × θ
- Velocity: v = r × ω
- Acceleration: a = r × α
2. MOMENT OF INERTIA (I)
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- Thin Hoop / Ring: I = MR²
- Solid Cylinder / Disk: I = 1/2 MR²
- Solid Sphere: I = 2/5 MR²
- Hollow Sphere: I = 2/3 MR²
3. DYNAMICS & ENERGY
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- Newton's 2nd Law (Rotation): Torque = I × α
- Torque Formula: Torque = r × F × sin(φ)
- Rotational Kinetic Energy: K = 1/2 × I × ω²
- Total Energy (Rolling): E = 1/2 mv² + 1/2 Iω²
4. MASTER SOLVER: ACCELERATION ON INCLINE
(Formula: a = (g sin θ) / (1 + I/MR²))
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- Hoop (Ring): a = 0.50 g sin θ.
- Cylinder (Disk): a = 0.67 g sin θ
- Solid Sphere: a = 0.71 g sin θ
5. EXAM PRO-TIPS
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* TIP 01: Static friction does NOT cause energy loss during pure rolling.
* TIP 02: A Solid Sphere always reaches the bottom faster than others.
* TIP 03: Total Kinetic Energy = Translational + Rotational.
© PHYSICS MASTER STUDY GUIDES 2026
(Advanced Placement & International Curriculum)
1. KINEMATICS COMPARISON
--------------------------------------------------
- Displacement: s = r × θ
- Velocity: v = r × ω
- Acceleration: a = r × α
2. MOMENT OF INERTIA (I)
--------------------------------------------------
- Thin Hoop / Ring: I = MR²
- Solid Cylinder / Disk: I = 1/2 MR²
- Solid Sphere: I = 2/5 MR²
- Hollow Sphere: I = 2/3 MR²
3. DYNAMICS & ENERGY
--------------------------------------------------
- Newton's 2nd Law (Rotation): Torque = I × α
- Torque Formula: Torque = r × F × sin(φ)
- Rotational Kinetic Energy: K = 1/2 × I × ω²
- Total Energy (Rolling): E = 1/2 mv² + 1/2 Iω²
4. MASTER SOLVER: ACCELERATION ON INCLINE
(Formula: a = (g sin θ) / (1 + I/MR²))
--------------------------------------------------
- Hoop (Ring): a = 0.50 g sin θ.
- Cylinder (Disk): a = 0.67 g sin θ
- Solid Sphere: a = 0.71 g sin θ
5. EXAM PRO-TIPS
--------------------------------------------------
* TIP 01: Static friction does NOT cause energy loss during pure rolling.
* TIP 02: A Solid Sphere always reaches the bottom faster than others.
* TIP 03: Total Kinetic Energy = Translational + Rotational.
© PHYSICS MASTER STUDY GUIDES 2026
