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

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

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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