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GATE 2023 PH – Question 41

Classical Mechanics · rigid body dynamics: inertia tensor, orthogonal transformations, Euler angles, torque free motion of a symmetric top · 2 marks · Multiple choice

A symmetric top has $I_1=I_2=2\alpha/3$, $I_3=2\alpha$ and no applied force. Its angular speed about the 3-axis is $\omega_3=1/8$ rad/s. With what angular frequency in rad/s does its angular velocity vector precess about the 3-axis?

  1. 2
  2. 3
  3. 5
  4. 7

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Show answer and explanation

Correct answer: (A) 2

Explanation

Torque-free Euler equations give $\Omega=(I_3-I_1)\omega_3/I_1=2\omega_3=1/4$ rad/s. A matches the factor 2, rather than the stated absolute frequency.