Question

What happens when a ballet dancer stretches her arms while taking turns?

Answer 1

The dancer stretches out her hands to slow down from spinning. It is based on the principle of conservation of angular momentum.

An object (the ballet dancer) rotating about an axis is the product of its momentum of inertia and its angular velocity (the speed of rotation and the orientation of the axis which the rotation takes place). The physical equation is L=Iw.

When the ballet dancer is spinning in a closed system, and no external forces are applied to it, it will have no change in angular momentum.

The conservation of angular momentum explains the angular acceleration of a ballet dancer as she brings her arms and legs close to the vertical axis of rotation. It’s the same with the spinning of an ice.

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Answer 2

When a ballet dancer stretches her arms while taking turns, her angular velocity decrease.

• Ballet dancers make use of law of conservation of angular momentum while spinning.
• When a ballet dancer stretches out her arms, her moment of inertia increases(I = mr^2).
• As moment of inertia increases, her angular velocity decreases.

         Let

                    $I_{1} =$ moment of inertia before stretching hands

                    $w_{1} =$ angular velocity before stretching hands

        and

                   $I_{2} =$ moment of inertia after stretching hands

                   $w_{2}$ = angular velocity after stretching hands

• Then, from law of conservation of angular momentum

                    $I_{1} w_{1} = I_{2} w_{2}$

                     $w_{2}=\frac{I_{1} }{I_{2} } w_{1}$

• Since $I_{2} > I_{1}$ ⇒ $w_{2}<w_{1}$