Rotational Motion Formulas for NEET: The Minimum Viable Core

Seedha Jawab: Har saal lakho droppers Rotational Motion (System of Particles) par 40 se 50 ghante barbad karte hain, jabki NEET me is chapter se sirf 2 questions (8 marks) aate hain. Complex inclined rolling, variable friction, aur toppling ke 20-step derivations NEET me kabhi nahi pooche jaate. Agar tumhara Mechanics weak hai, toh pure chapter ko chhodne ki zaroorat nahi hai. Sirf 6 Master Formulas yaad karo aur in 8 marks ko pocket me daalo. Yahan hai Rotational Motion ka Minimum Viable Core.

Hamare decadal weightage audit NEET 2027 Chapter-Wise Weightage: The 45-Chapter Cutoff Guarantee aur The Physics Formula Book for NEET: Recall Under Clock Pressure me humne dikhaya tha ki Rotational Motion Tier-4 (Low Marks / High Effort) quadrant me aata hai.

Is chapter me PhD nahi karni hai. Sirf wahi 6 formulas padhne hain jinpar NTA 10 saal se baar-baar sawaal repeat kar raha hai.

The 6 Master Formulas (The Minimum Viable Core)

1. Moments of Inertia of 4 Standard Bodies

NTA 90% sawaal inhi chaar shapes par poochta hai:

Ring / Thin Cylindrical Shell: $I_{\text{cm}} = MR^2$
Circular Disc / Solid Cylinder: $I_{\text{cm}} = \frac{1}{2}MR^2$
Solid Sphere: $I_{\text{cm}} = \frac{2}{5}MR^2$
Hollow Sphere (Spherical Shell): $I_{\text{cm}} = \frac{2}{3}MR^2$

2. Theorems of Moment of Inertia

Parallel Axis Theorem: $I = I_{\text{cm}} + Md^2$ (Valid for any shape, but $I_{\text{cm}}$ must be through center of mass).
Perpendicular Axis Theorem: $I_z = I_x + I_y$ (Valid ONLY for flat laminar 2D planar bodies).

3. Torque Equation (Rotational Newton 2nd Law)

$$\vec{\tau} = \vec{r} \times \vec{F} = I\vec{\alpha}$$

Scalar form: $\tau = r F \sin\theta$.
Work done by torque: $W = \int \tau d\theta = \tau \cdot \Delta\theta$.

4. Rotational Kinetic Energy

$$K_{\text{total}} = K_{\text{trans}} + K_{\text{rot}} = \frac{1}{2}Mv_{\text{cm}}^2 + \frac{1}{2}I_{\text{cm}}\omega^2$$

For pure rolling ($v = \omega R$):

$$K_{\text{total}} = \frac{1}{2}Mv^2 \left(1 + \frac{k^2}{R^2}\right)$$

Where $k$ is the radius of gyration.

5. Conservation of Angular Momentum

$$L = I\omega = \text{constant} \quad (\text{when } \tau_{\text{ext}} = 0)$$

Typical NEET Question: Disc rotating at $\omega_1$, another disc of inertia $I_2$ is placed on it gently. Common angular velocity:

$$\omega_{\text{common}} = \frac{I_1 \omega_1}{I_1 + I_2}$$

6. Acceleration and Velocity on Inclined Plane

Pure rolling down an incline of angle $\theta$:

$$a = \frac{g\sin\theta}{1 + \frac{k^2}{R^2}}, \qquad v = \sqrt{\frac{2gh}{1 + \frac{k^2}{R^2}}}$$

Topper Shortcut Rule: Jiska $\frac{k^2}{R^2}$ sabse chhota hoga, uska acceleration sabse bada hoga aur wo sabse pehle neeche aayega:

$$\text{Solid Sphere } (0.4) > \text{Disc } (0.5) > \text{Hollow Sphere } (0.67) > \text{Ring } (1.0)$$

Action Plan for Weak Students

In 6 formulas ko ek single A4 sheet par likho.
Hamare Top 90 Numerical Profiles se Rotational Motion ke 15 questions lagao.
Complex toppling ya curved track questions ko skip karke apna baki time Modern Physics me invest karo.