Question Bank MCQ • 2 Marks Section 2: Classical Mechanics Classical Mechanics - Module 4

QB_PH_045: Classical Mechanics - Module 4

Question Statement

For a torque-free symmetric top ($I_1 = I_2 \ne I_3$), the precession frequency $\Omega$ of angular velocity about the symmetry axis is:
(A) \frac{I_1 - I_3}{I_1} \omega_3
(B) \frac{I_3 - I_1}{I_3} \omega_3
(C) \frac{I_1 + I_3}{I_1} \omega_3
(D) \frac{I_3}{I_1} \omega_3
Correct Answer
A
Verified Key

Step-by-Step KaTeX Derivation & Detailed Explanation

### Solution: Euler equations: $I_1 \dot{\omega}_1 = (I_1 - I_3) \omega_2 \omega_3 \implies \Omega = \frac{I_1 - I_3}{I_1}\omega_3$.
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