Respuesta :
The ratio of the skater's moment of inertia when they have their arms extended to when their arms are not is r²/(r+r₁)².
The moment of inertia of any particular object can be defined as the opposition displayed by the object in question whenever its speed of rotation is changed when any external(turning) force is applied.
Let us assume that the moment of inertia of the skater when they don't extend their arms be = mr² (i)
Here, r is the radius of their body with their arms squeezed in.
The moment of inertia when the skater will extend their arms outwards is going to be = m(r+r₁)² (ii)
Here, r₁ is the radius of the hands when they are extended.
Comparing and equating (i) and (ii), we get -
Ratio = r²/(r+r₁)² (m is common for both so it gets canceled)
Henceforth, here is the ratio for when the skater has their arms extended to when their arms are not.
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