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418 CHAPTER 13 Dynamics of a Rigid Body

TORQUE VECTOR T r F z (13.35)
F

O y
r u

t
x

EQUATION OF ROTATIONAL MOTION FOR d L
VECTOR ANGULAR MOMENTUM dt (13.47)

GYROSCOPIC PRECESSION ANGULAR VELOCITY rMg
(13.51)
where r is the distance from the point of contact p L
to the center of mass.
p
L

QUESTIONS FOR DISCUSSION

1. Suppose you push down on the rim of a stationary phono- 7. Why do helicopters need a small vertical propeller on their tail?
graph turntable. What is the direction of the torque you exert
8. The rate of rotation of the Earth is subject to small seasonal vari-
about the center of the turntable?
ations. Does this mean that angular momentum is not conserved?
2. Many farmers have been injured when their tractors suddenly
9. Why does the front end of an automobile dip down when the
flipped over backward while pulling a heavy piece of farm
automobile is braking sharply?
equipment. Can you explain how this happens?
10. The friction of the tides against the ocean coasts and the
3. Rifle bullets are given a spin about their axis by spiral grooves
ocean shallows is gradually slowing down the rotation of the
(“rifling”) in the barrel of the gun. What is the advantage of this?
Earth. What happens to the lost angular momentum?
4. You are standing on a frictionless turntable (like a phonograph
11. An automobile is traveling on a straight road at 90 km/h.
turntable, but sturdier). How can you turn 180 without leav-
What is the speed, relative to the ground, of the lowermost
ing the turntable or pushing against any exterior body?
point on one of its wheels? The topmost point? The midpoint?
5. If you give a hard-boiled egg resting on a table a twist with
12. A sphere and a hoop of equal masses roll down an inclined
your fingers, it will continue to spin. If you try doing the same
plane without slipping. Which will get to the bottom first? Will
with a raw egg, it will not. Why?
they have equal kinetic energy when they reach the bottom?
6. A tightrope walker uses a balancing pole to keep steady
13. A yo-yo rests on a table (Fig. 13.26). If you pull the string
(Fig. 13.25). How does this help?
horizontally, which way will it move? If you pull vertically?
(a) (b) String pulls
vertically.
String pulls
horizontally.

FIGURE 13.25 A tightrope walker. FIGURE 13.26 Yo-yo resting on a table. (a) String pulls horizontally. (b) String
pulls vertically.