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A disc is spinning with an angular velocity w rad/s about the axis of spin. The couple applied to the disc causing precession will be: (where I = Mass moment of inertia of the disc, and wP = Angular velocity of precession of the axis of spin)

A disc is spinning with an angular velocity w rad/s about the axis of spin. The couple applied to the disc causing precession will be: (where I = Mass moment of inertia of the disc, and wP = Angular velocity of precession of the axis of spin) Correct Answer <span class="py-2">Iωω<sub>p</sub></span>

Explanation:

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Axis of spin:

  • The disc is rotated about a particular axis, that axis of rotation (ω) referred to as the axis of spin.
  • In general, the axis of rotation of the disc is considered as the axis of spin as a reference axis for the further calculation.

Axis of precession:

  • The motion of direction of initial angular momentum is known as precession (ωp) and axis about which precession takes place is known as the axis of precession.

Applied gyroscopic couple:

  • The couple which appears due to change in the direction of angular momentum is known as an active gyroscopic couple or precession couple.
  • The active gyroscopic couple or precession couple is given by,
  • T = Iωωp

where ω = angular velocity of the disc, ωp  = angular velocity of precision of axis of spin and  I = mass momentum inertia of disc.  

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