# A woman is sitting on a spinning seat of a piano stool with her arms folded. Ignore any friction in the spinning stool. What happens to her

Question

A woman is sitting on a spinning seat of a piano stool with her arms folded. Ignore any friction in the spinning stool. What happens to her angular velocity and angular momentum when she extends her arms outward?

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1 year 2021-09-04T11:00:16+00:00 1 Answers 181 views 0

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:

$$L=I.\omega$$

where:

$$I=$$ moment of inertia (second moment of mass that depends upon the radial distance of the mass from the center of rotation)

$$\omega=$$ 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.

$$I’\times \omega’=I\times \omega$$