Answer:
The angular velocity of the woman will decrease when she extends her arms outwards.
Explanation:
We know that the angular momentum of a body is the product of its angular velocity and the moment of inertia.
So, mathematically:
[tex]L=I.\omega[/tex]
where:
[tex]I=[/tex] moment of inertia (second moment of mass that depends upon the radial distance of the mass from the center of rotation)
[tex]\omega=[/tex] angular velocity
When the woman extends her arms she increases the radial distance of her mass form the axis of rotation thus increasing the moment of inertia of her body. As the angular momentum in this case remains constant so proportionately the angular velocity of her body increases.
[tex]I'\times \omega'=I\times \omega[/tex]
The angular velocity will increase and angular momentum remains constant, when she extends her arms outward.
The given problem is based on the concept of angular momentum. The angular momentum of a body is the product of its angular velocity and the moment of inertia. So, mathematically:
[tex]L = I \times \omega[/tex]
Here,
I is the moment of inertia.
[tex]\omega[/tex] is the angular velocity.
Note: - The moment of inertia (I) depends on the radial distance and mass of object.
So in the given problem, when the woman extends her arms she increases the radial distance of her mass and form the axis of rotation. Thereby increasing the moment of inertia of her body. As the angular momentum in this case remains constant so proportionately the angular velocity of her body increases.
Thus, we can conclude that the angular velocity increases and angular momentum remains constant, when she extends her arms outward.
Learn more about the angular momentum here:
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