Rotational Motion

Olympiad (NSEP) level, one or more correct, hard

4 of 280

Question 4 of 280

A spinning symmetrical top of mass MM with moment of inertia IsI_s about its symmetry axis spins with high angular velocity Ω\Omega. The center of mass is at distance LL from pivot. Which of the following statements are CORRECT?

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Answer: (A) Precession angular velocity increases as spin velocity Ω\Omega decreases, (B) Precession frequency is inversely proportional to the spin angular velocity Ω\Omega, (C) The gyroscopic precession angular velocity is Ωp=MgLIsΩ\Omega_p = \frac{M g L}{I_s \Omega}, (D) The torque about pivot is directed horizontally perpendicular to spin axis

τ=MgL=IsΩΩp  ⟹  Ωp=MgLIsΩ\tau = M g L = I_s \Omega \Omega_p \implies \Omega_p = \frac{M g L}{I_s \Omega}. Torque τ⃗=r⃗×Mg⃗\vec{\tau} = \vec{r} \times M\vec{g} acts horizontally, causing horizontal precession.
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