Question

A dancer on ice spins faster when she fold her arms. This is due to

Answer 1

Answer:

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Explanation:

Concept 1

Inertia I of a discrete the mass m at distance r from an axis is given by (about the axis)

I=mr2

⇒ I∝r2

So, when r decreases inertia I decreases

Concept 2

Angular momentum (L) is a conserved quantity and remains constant when external. Torque on a body is zero

dtdL=τ

if τ=0

⇒L= constant

we know that

∣∣∣∣L∣∣∣∣=I.ω⇒ω=I∣∣∣∣L∣∣∣∣⇒ω∝I1

Now

when the dancer folds her arms basically whe is decreasing her inertia

And,

Since ω∝I1

So, decreasing of inertia (I), results, in inrease of angular velocity hence

The faster spin faster due to constant momentum and increase in angular velocity

Answer 2

A dancer on ice spins faster when she folded her arms. This is due to an increase in energy and an increase in angular momentum.

Explanation:

• Dancers make use of the law of conservation of angular momentum while spinning. As the moment of inertia increases, and angular velocity decreases.
• Whenever the dancer folds her arms and brings them towards the centre of the body the moment of inertia decreases as a result of the angular velocity increases.
• During the course of their performance, an ice skater, a ballet dance or an acrobat take use of the principle of conservation of angular momentum.