WEBVTT

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This is Giancoli Answers
with Mr. Dychko.

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The angular momentum of
the figure skater is

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their moment of inertia times
their angular velocity.

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Moment of inertia for a cylinder is one-half
mass times its radius squared

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and the height of the figure skater is
not important,

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we only care about the radius
or the distance

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from the axis of rotation which is
the middle of her body

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to the outside of her body—

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maybe guess from her neck to her shoulder
is probably this distance <i>r</i> here.

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So that's one-half times 48 kilograms times
0.15 meters squared

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times 3 revolutions per second written in
radians per second by multiplying

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by 2<i>π</i> radians per revolution

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and we get 1.0 times 10 to the 1 kilogram
meter squared per second.

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And I wrote this in scientific
notation just to

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be clear that there are two
significant figures;

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if I had just wrote the number 10 that
would be one significant figure.

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So torque required to bring this
figure skater to a stop

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is gonna be the rate of change of
angular momentum

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so that's final angular momentum minus
initial divided by time

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and there is no final angular momentum
because they come to a stop

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and so it's negative <i>L i</i> over <i>t</i>.

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So that's negative 10.1788 kilogram
meter squared per second

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divided by 4 seconds which is negative
2.5 newton meters of torque;

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the negative sign being the opposite to
the initially positive angular velocity.

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So this torque is in the opposite direction
to the initial angular velocity.