Question
Download Solution PDFIf the moment of inertia of a rotating body is increased then what will be the effect on the angular velocity?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFCONCEPT:
- 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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