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408 CHAPTER 13 Dynamics of a Rigid Body

A pirouette performed by a figure skater on ice provides a nice illustration of the
Skater has a larger
(a)
moment of inertia conservation of angular momentum. The skater begins the pirouette by spinning
when arms are out…
about her vertical axis with her arms extended horizontally (see Fig. 13.10a); in this
configuration, the arms have a large moment of inertia. She then brings her arms close
to her body (see Fig. 13.10b), suddenly decreasing her moment of inertia. Since the ice
is nearly frictionless, the external torque on the skater is nearly zero, and therefore the
angular momentum is conserved. According to Eq. (13.26), a decrease of I requires
an increase of to keep the angular momentum constant. Thus, the change of con-
figuration of her arms causes the skater to whirl around her vertical axis with a dramatic
increase of angular velocity (see Fig. 13.11).
Like the law of conservation of translational momentum, the Law of Conservation
of Angular Momentum is often useful in the solutions of problems in which the forces
are not known in detail.

…and a smaller moment
of inertia and a larger
(b)
angular velocity when
arms are in. EXAMPLE 9 Suppose that a pottery wheel is spinning (with the motor dis-
engaged) at 80 rev/min when a 6.0-kg ball of clay is suddenly
dropped down on the center of the wheel (see Fig. 13.12). What is the angular
velocity after the drop? Treat the ball of clay as a uniform sphere of radius 8.0 cm.
2
The pottery wheel has a moment of inertia I 7.5 10 2 kg m . Ignore the
(small) friction force in the axle of the turntable.
SOLUTION: Since there is no external torque on the system of pottery wheel and
clay, the angular momentum of this system is conserved.The angular momentum
before the drop is

L I (13.30)
FIGURE 13.10 Figure skater performing
a pirouette. (a) Arms extended. (b) Arms where is the initial angular velocity and I the moment of inertia of the pottery
folded against body. wheel. The angular momentum after the drop is

œ œ
L I (13.31)
œ
where is the final angular velocity and I the moment of inertia of pottery wheel
and clay combined. Hence

I I (13.32)
œ œ
from which we find

I
œ
(13.33)
I œ
The wheel is initially rotating with angular velocity

80 rev
2p f 2p 8.4 radians/s
60 s

The moment of inertia of the pottery wheel is given,

FIGURE 13.11 A figure skater whirling I 7.5 10 2 kg m 2
at high speed.