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Question

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

A
decrease in energy and increase in angular momentum
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B
increase in energy and increase in angular momentum
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C
increase in energy and decrease in angular momentum
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D
constant angular momentum and increase in KE.
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Solution

The correct option is A decrease in energy and increase in angular momentum
Concept 1
Inertia I of a discrete the mass m at distance r from an axis is given by (about the axis)
I=mr2
Ir2
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
dLdt=τ
if τ=0
L= constant
we know that
L=I.ωω=LIω1I
Now
when the dancer folds her arms basically whe is decreasing her inertia
And,
Since ω1I
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

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