When a figure skater spinning with her arms outstretched brings her arms closer to her body?

Question

she begins to rotate at a much faster rate. When she stretches out her arms once again, she rotates more slowly. Which of the following best explains this phenomenon?

This is what I have to chose from

When the skater's arms are out, she has more air resistance, so she moves more slowly.

The act of bringing her arms closer to her body pushes her around more quickly.

With her arms together, she has more weight pressing down on a smaller area, which allows her to move faster.

With her arms outstretched, her moment of inertia is larger, so when she brings them in, her angular velocity much increase due to the conservation of angular momentum,

She must do work to bring her arms into her body, and so that work goes into increasing her angular velocity.

Can anyone help me please?

Answer 1

Conservation of angular momentum:

Rotational velocity before times moment of inertia before
=
Rotational velocity after times moment of inertia after.

So if you decrease moment of inertia (and conserve angular momentum), the spinning must speed up to compensate.

Answer 2

With her arms outstretched, her moment of inertia is larger, so when she brings them in, her angular velocity much increase due to the conservation of angular momentum

(i)when a person is rotating on a block outstrsetched her arms her angular momentum would less so the no .of rotations done by her would be less.
(ii)If he keeps her hands close then the angular momentum would be more so she can make more rotations than the above case(i).

Answer 3

This [edited] statement from your list best explains the phenomenon:

"With her arms outstretched, her moment of inertia is larger, so when she brings them in, her angular velocity mu[st] increase due to the conservation of angular momentum."

If the Moment of Inertia is denoted by ' MI,' and the angular rate of rotation is ' w ' rad/s, then the angular momentum ' AM ' is given by:

AM = MI*w.

So, if AM is conserved but the skater has different moments of inertia at different times,

AM = MI1*w1 = MI2*w2.

Thus w1 / w2 = MI2 / MI1; that is to say, the angular rotation rate is INVERSELY proportional to the moment of inertia.

Although the arms are not very massive relative to the entire mass of the skater, in calculating the moment of inertia each element of mass is weighted by the SQUARE of its distance from the rotation axis. Thus, pulling the arms in tightly can indeed reduce the moment of inertia considerably. That is why and how the very large spin rate speed-ups of a skater can be obtained.

Live long and prosper.

Answer 4

This one gets my vote.

With her arms outstretched, her moment of inertia is larger, so when she brings them in, her angular velocity much increase due to the conservation of angular momentum.

Answer 5

Its the conservation of angular momentum thing. For you to make a wider circle you have to travel more, or use more force. When she pulls her arms close, she makes her circle smaller. This way she can spin faster because she doesn't have to use so much force. Basically