If the moment of inertia of a rotating body is increased then what will be the effect on the angular velocity?

  1. It will increase
  2. It will decrease
  3. There will be no effect
  4. First increase and then decrease

Answer (Detailed Solution Below)

Option 2 : It will decrease
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Detailed Solution

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CONCEPT:

  • The angular momentum of a particle rotating about an axis is defined as the moment of the linear momentum of the particle about that axis.
  • It is measured as the product of linear momentum and the perpendicular distance of its line of action from the axis of rotation.
  • The relation between the angular momentum and moment of inertia is given by

L = Iω

Where I = moment of inertia, L = angular momentum, and ω = angular velocity.

EXPLANATION:

  • If there is no external torque acting on system then initial angular momentum (Linitial) of system is equal to final momentum (Lfinal).
  • Hence, the angular momentum in a closed system is a conserved.

∴ Iω = constant

⇒ I ∝ 1/ω

i.e. Moment of inertia is inversely proportional to the angular velocity.

  • Hence if the moment of inertia of a rotating body is increased then the angular velocity decreases.
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