Though most tennis players generally strive to
strike the ball on the racket's vibration node, more
commonly known as the "sweet spot," many players
are unaware of the existence of a second, lesser-
known location on the racket face, the center of per-
cussion, that will also greatly diminish the strain on a
player's arm when the ball is struck.
In order to understand the physics of this sec-
ond sweet spot, it is helpful to consider what would
happen to a tennis racket in the moments after impact
with the ball if the player's hand were to vanish at the
moment of impact. The impact of the ball would cause
the racket to bounce backwards, experiencing a trans-
lational motion away from the ball. The tendency of
this motion would be to jerk all parts of the racket,
including the end of its handle, backward, or away
from the ball. Unless the ball happened to hit the rack-
et precisely at the racket's center of mass, the racket
would additionally experience a rotational motion
around its center of mass-much as a penny that has
been struck near its edge will start to spin. Whenever
the ball hits the racket face, the effect of this rotational
motion will be to jerk the end of the handle forward,
towards the ball. Depending on where the ball strikes
the racket face, one or the other of these motions will
However, there is one point of impact, known
as the center of percussion, which causes neither
motion to predominate; if a ball were to strike this
point, the impact would not impart any motion to the
end of the handle. The reason for this lack of motion is
that the force on the upper part of the hand would be
equal and opposite to the force on the lower part of
the hand, resulting in no net force on the tennis play-
ers' hand or forearm. The center of percussion consti-
tutes a second sweet spot because a tennis player's
wrist typically is placed next to the end of the racket's
handle. When the player strikes the ball at the center
of percussion, her wrist is jerked neither forward nor
backward, and she experiences a relatively smooth,
comfortable tennis stroke.
The manner in which a tennis player can
detect the center of percussion on a given tennis rack-
et follows from the nature of this second sweet spot.
The center of percussion can be located via simple
trial and error by holding the end of a tennis racket
between your finger and thumb and throwing a ball
onto the strings. If the handle jumps out of your hand,
then the ball has missed the center of percussion.
1. What is the primary message the author is trying to convey?
(A) a proposal for an improvement to the design of tennis rackets
(B) an examination of the differences between the two types of sweet spot
(C) a definition of the translational and rotational forces acting on a tennis racket
(D) a description of the ideal area in which to strike every ball
(E) an explanation of a lesser-known area on a tennis racket that dampens unwanted vibration
2. According to the passage, all of the following are true of the forces acting upon a tennis
racket striking a ball EXCEPT
(A) The only way to eliminate the jolt that accompanies most strokes is to hit the ball on the center of
(B) The impact of the ball striking the racket can strain a tennis player's arm.
(C) There are at least two different forces acting upon the racket.
(D) The end of the handle of the racket will jerk forward after striking the ball unless the hall strikes the
racket's center of mass.
(E) The racket will rebound after it strikes the ball.
3. What is the primary function served by paragraph two in the context of the entire passagd
(A) to establish the main idea of the passage
(B) to provide an explanation of the mechanics of the phenomenon discussed in the passage
(C) to introduce a counterargument that elucidates the main idea of the passage
(D) to provide an example of the primary subject described in the passage
(E) to explain why the main idea of the passage would be useful for tennis players
4. The author mentions "a penny that has been struck near its edge" in order to
(A) show how the center of mass causes the racket to spin
(B) argue that a penny spins in the exact way that a tennis racket spins
(C) explain how translational motion works
(D) provide an illustration of a concept
(E) demonstrate that pennies and tennis rackets do not spin in the same way
5. Which of the following can be inferred from the passage?
(A) If a player holds the tennis racket anywhere other than the end of the handle, the player will
experience a jolting sensation.
(B) The primary sweet spot is more effective at damping vibration than the secondary sweet spot.
(C) Striking a tennis ball at a spot other than the center of percussion can result in a jarring feeling.
(D) Striking a tennis ball repeatedly at spots other than a sweet spot leads to "tennis elbow."
(E) If a player lets go of the racket at the moment of impact, the simultaneous forward and backward
impetus causes the racket to drop straight to the ground.OA
: E A B D C
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