In addition to the forces that produce motion, a number of forces
act to modify motion in some manner. These modifying forces must
be considered when studying the kinetics of linear motion. When
the kinesiological analysis model presented in Chapter 1 is applied
to a motor skill, the forces that modify motion must be included
in any discussion of the nature of the forces involved. Six of these
forces are commonly categorized as follows:
For purposes of discussion in this chapter, an additional category
of elasticity and rebound has been added.
In what came to be known as the Law of Gravitation, Newton (remember
the apple) was the first to point out that all bodies are attracted
to each other in direct proportion to their masses and in inverse
proportion to the square of the distance between them. The amount
of this attraction between bodies on earth is negligible except
for the attraction between the earth itself and the bodies on it.
Because of the earth’s huge mass, this attraction is quite
noticeable. The force is called gravity, and it is measured as the
weight of the body applied through the center of gravity of the
body and directed toward the earth’s axis (Figure 12.16).
The closer a body is to the earth’s center, the greater
is the gravitational pull and, therefore, the more it weighs. When
the body moves far enough away from the earth’s center,
such as to the moon, the decrease in the gravitational pull is apparent,
as in the ease of giant leaps made by astronauts. The mass of the
body is the same as on earth, but the weight has decreased in proportion
to the gravitational pull. The relation between weight, mass, and
gravity is represented in equation form as w = mg. The force of weight must be considered
in all motion analyses.
Figure 12.16Graphic Jump Location
Gravitational force is measured as the weight of the
body applied through the center of gravity of the body and directed
toward the center of the earth.
As Newton’s third law states, for every action there
is an equal and opposite reaction. Anytime a force is exerted on
an object, that object will exert a force back. As you sit and read
this section, you are exerting a force on a chair and the chair
is exerting an equal and opposite force on you. If the chair did
not exert an equal and opposite force, you would be falling toward
the floor. If you are sitting still, the ground reaction force is
equal to your body weight. Likewise, when you walk, run, or jump,
the ground pushes back on you with the same force with which you
exert on the floor. In Figure 12.17 the high jumper exerts a force
on the ground (action), and the ground exerts a force on the jumper’s
foot (reaction force).
Figure 12.17Graphic Jump Location
Example of normal reactive force. As the jumper pushes
down on the ground, the ground pushes back.
Without the reactive force there would be no motion. You cannot
walk without the ground reaction force. When the heel strikes the
ground, the ground brings the foot to rest so the body can pass
over the planted foot. Then the ground reaction force pushes back
against the toe at push-off. Ground reaction force is usually measured
with a force platform and during jogging can be as high as two to
three times body weight. If a book (4.45 N) is sitting on the floor,
the ground reaction force is equal to the weight of the book (4.45
N). If you were to push directly down on the book, the ground reaction
force would be the sum of the weight of the book plus the pushing-down
force. If the force that you exerted on the book was not directly
down, but at an angle, the ground reaction force would be the sum
of only that part of the force acting downward plus the weight of
Friction is the force that opposes
efforts to slide or roll one body over another. Without friction
it would be impossible to walk or run or do much of any kind of
moving. On the other hand, friction increases the difficulty of
moving objects about with its deterrent effect. There are numerous examples
in which we attempt to increase friction
for more effective performance. The use of rubber-soled shoes on
hardwood floors or wet decks, spikes on golf shoes, and rubber knobs
on hiking boots improve friction with the supporting surface. Chalk
on the gymnast’s hands, on work gloves, and on cloth grips
on tennis rackets are all used to decrease slippage. Even the surfaces
of balls are designed to increase friction through irregularities
such as the fuzz on the tennis ball or the dimples on a golf ball.
Attempts to decrease friction are also evident in physical activity.
The sole of one of a bowler’s shoes is made to have little
friction so that it can slide more easily in the approach. Sharp
ice skates apply pressure on the ice and cause slight melting, thus
making it easier for the skates to move across the ice. Ice covered
with a slight film of water is more slippery than colder, drier
ice. Skis are waxed, bicycles are greased, and in-line skates have
ball bearings, each for the purpose of minimizing the retardant
effect of friction.
The amount of friction between one surface and another depends
on the nature of the surfaces and the forces pressing them together.
Generally speaking, smooth surfaces have less friction than rough
surfaces. The area of surfaces in contact with each other does not
affect friction. A footlocker pulled along on one end would take
as much force to pull as one on its side. An empty footlocker, however,
would take less force than one full of books. Friction
is proportional to the force pressing two surfaces together.
In Figure 12.18 the book is pressing down on the table with a
force (W) equal to its weight. The
reactive force of the table pushing up against the book is called
the normal force (N). The normal force
acts perpendicular to the support surface and in this case is equal
and opposite to the weight of the book. The maximum force that can
be applied to the book before it begins
to slide is called the force of static friction (Fmax).
The ratio of the force of static friction to the normal force is
a quantity called the coefficient of static friction (μs).
Figure 12.18Graphic Jump Location
The coefficient of friction is the ratio between the
force needed to overcome the friction P to
the force holding the surfaces together W.
The symbol μs (mu) represents the coefficient
of static friction and is an experimentally determined quantity
that is a constant for any two surfaces. The larger the coefficient,
the more the surfaces cling together and the more difficult it is
for the two surfaces to slide over each other. Police officers use
this information every day in investigating automobile accidents.
To determine how fast a car was going, they look to the length of
the skid marks and determine how much friction (the coefficient of
friction) was between the tires and the road. This is achieved experimentally
through use of a drag sled. A portion of a tire filled with concrete
to approximate the weight on one tire of a car is pulled along the
road by a spring scale. The reading of the spring scale just before
the sled moves is recorded as Fmax.
The total weight of the car divided by four is the N, and the coefficient of friction
is Fmax/N. From this information the police
officers can tell how fast the car was going and if it was traveling
over the posted speed limit.
From an exercise science perspective, friction is a very important
concept and is taken into consideration when looking at shoe to
floor interface. It is used to answer such questions as which court
shoes give better traction on hardwood floors or clay tennis courts.
Up to this point the discussion has centered on static friction,
which is the amount of attraction between two surfaces that must
be overcome for one of those surfaces to begin to move along the other.
Once motion has been achieved, other types of friction take over
such as sliding friction and rolling friction. Static friction will
always be greater than sliding friction or rolling friction for a
given set of surface conditions. It is easier to keep something
moving than to get it moving in the first place. As the name implies, sliding friction is a measure of the
resistance of one surface to continue to slide along another and
can be used to explain how far from a base a player needs to begin
a slide. Rolling friction considers
how easily one surface can continue to roll over another surface.
Rolling friction helps soccer players and golfers determine how
a ball will react on short grass versus high thick grass, and helps
people determine which surface is better for in-line skating. The
smaller the coefficient, the easier it is for the two surfaces to
begin sliding or rolling over each other. A coefficient of 0.0 would
indicate completely frictionless surfaces. The equation also shows
that the coefficient of friction is totally dependent on the force
holding the surfaces together (N) and
the force needed to slide one surface over the (Fmax).
The coefficient will decrease as Fmax decreases.
The coefficient of friction between two objects may also be found
by placing one object on the second and tilting the second until
the first starts to slide. The tangent of the angle of the second object
with the horizontal is the coefficient of friction (Figure 12.19).
An interesting application of the use of μ can
be seen with respect to the gripping power of basketball shoes.
The amount of lean a player may safely take is equal to the angle θ that
the player makes with the vertical, whose tangent = is
the amount of horizontal force needed to cause the feet to start sliding horizontally,
and W is the weight of the player (Figure
12.20). Shoes allowing a greater lean would certainly afford their
wearers an advantage in the game. For this information to be of
use to shoe manufacturers, however, a standard type of floor surface
would have to be determined.
Figure 12.19Graphic Jump Location
An inclined plane may be used to determine the coefficient
of friction μ between two surfaces.
Figure 12.20Graphic Jump Location
The amount of lean a basketball player can safely assume
depends on the friction between the floor and his or her shoes.
Objects that rebound from each other do so in a fairly predictable
manner. The nature of a rebound is governed by the elasticity, mass,
and velocity of the rebounding surfaces, the friction between the
surfaces, and the angle with which one object contacts the second.
Anytime two or more objects come into contact with each other,
some distortion or deformation occurs. Whether or not the distortion
is permanent depends on the elasticity of the interacting objects.
Elasticity is the ability of an object to resist distorting influences
and to return to its original size and shape when the distorting
forces are removed. The force that acts on an object to distort
it is called stress. The distortion
that occurs is called strain and is
proportional to the stress causing it. Stress may take the form
of tension, as in the stretching of a spring; compression, as in
the squeezing of a tennis ball (Figure 12.21); bending, such as the
bending of a fencing foil; or torsion, as in the twisting of the
spring. In all cases the object tends to resume its original shape
when the stress is removed. If the stress is too large, the elastic limit
of the object is exceeded and permanent distortion occurs.
Substances vary in their resistance to distorting forces and
in their ability to regain their original shapes after being deformed.
One usually thinks of a material such as rubber as being highly
elastic because it yields easily to a distorting force and returns
to its original shape. Actually, substances that are hard to distort
and return perfectly to their original shapes are more elastic. Gasses,
liquids, highly tempered steel, and brass are examples. In comparing
the elasticity of different substances, coefficients of elasticity
are used. A coefficient of elasticity or restitution is defined
as the stress divided by the strain.
The coefficient of elasticity most commonly determined in sports
activities is that caused in the compression of balls. If one drops
a ball onto a hard surface like a floor, the coefficient of restitution
may be determined by comparing the drop height with the bounce height
in the equation
where e = coefficient
of restitution or elasticity. The closer the coefficient approaches
1.0, the more perfect the elasticity. Rules require that a basketball
should be inflated to rebound to a height of 49 to 54 inches at
its top when its bottom is dropped from a height of 72 inches. For
the maximum bounce height, this is a coefficient of .781. In comparison,
a volleyball dropped from the same height and inflated to 6 psi
(pounds per square inch) rebounds to 51 inches and has a coefficient
of .84. A tennis ball has a coefficient of .73, and a leather-covered
softball one of .46.
The coefficient of elasticity may also be found in another way.
Because the Law of Conservation of Momentum states that the total
momentum in any impact between two objects must remain the same,
the momentum of one object may be reduced, so long as the momentum
of the other object increases proportionately. If the objects are
numbered 1 and 2 and it is assumed that mass of the objects remains
constant, it is possible to find the coefficient of elasticity by
using the change in velocity of the two objects:
where vf2 and vf1 are the velocities after
impact and vi1 and vi2 are the velocities before
An elastic object dropped vertically onto a rebounding surface
will compress uniformly on its underside and rebound vertically
upward. An elastic object that strikes a rebounding surface obliquely
will compress unevenly on the bottom and rebound at an oblique angle.
The size of the rebound angle compared with that of the striking
angle depends on the elasticity of the striking object and the
friction between the two surfaces. The rebound of a perfectly elastic
object is similar to the reflection of light: The
angle of incidence (striking) is equal to the angle of reflection
(rebound) (Figure 12.22). Variations from this ideal are to
be expected as the coefficient of restitution varies. Low coefficients
will generally produce angles of reflection greater than angles
For example, an underinflated volleyball will not have a great
coefficient of restitution. It will therefore rebound at an angle
much less, or much closer to the floor, than the striking angle.
The coefficient of restitution acts to affect the vertical component
of rebound. In rebound at an oblique angle, friction affects the
horizontal component of the rebound. An increase in friction will
produce a decrease in the angle of rebound. It is possible to produce
an angle of rebound equal to the angle of incidence by decreasing
both the horizontal component (increased friction) and the vertical
component (elasticity) proportionately. If the proportions between
the two components are constant, the angle of rebound will equal
the angle of incidence, but the resultantvelocity of the object
after impact will be decreased.
Effects of Spin
Spin also influences rebounding angles. Balls thrown with topspin
will rebound from horizontal surfaces lower and with more horizontal
velocity than that with which they struck the surface. They will
tend to roll farther also, an action often desirable on long golf
drives. Balls hitting a horizontal surface with backspin rebound
at a higher bounce and are slower. Balls with backspin also roll
for shorter distances than those with topspin or no spin. Because
of the compression of the ball and the friction between it and the
surface, a ball with no spin hitting the surface at an angle will
develop some topspin on the rebound, and a ball hitting with topspin
will develop greater topspin upon rebounding. With backspin, however,
the spin may be completely stopped or reversed. A ball with sidespin
will rebound in the direction of the spin. A ball spinning or curving
to the right will “kick” to the right upon rebounding,
and a left-spinning ball will do the reverse.
When spinning balls hit vertical surfaces, such as a basketball
backboard or a racquetball court wall, they respond in relation
to the surface in the same manner as with horizontal surfaces. When the
vertical surface is struck from below, a ball with no spin or topspin
will have added spin on rebound, and the angle of reflection will
be greater than the angle of incidence. With backspin the spin will
stop or reverse and the angle of reflection will be less than the
incidence angle. For this to be true, a backspinning ball approaching
a vertical wall from above must be regarded as moving with topspin
in relation to the rebounding surface. Similarly, a topspinning
ball hitting the vertical surface from above is in actuality spinning
backward with respect to the rebounding surface.
When a spinning ball meets a forward-moving object, as in tennis
or table tennis, the ball will rebound in a direction that results
from the forces acting on it at impact. For example, a ball with topspin
striking a stationary vertical surface head-on will rebound upward.
That same ball (with topspin) striking a moving vertical surface,
like a tennis racket, will also rebound upward, but not as much,
because the resultant rebound has a horizontal force component from
the forward-moving tennis racket. Nevertheless, the upward direction
may be sufficient to send the ball out of bounds. To counteract
the upward direction, the racket face can be turned obliquely downward, thus
adding a downward compensating force component as well as changing
the spin of the ball.
The resultantforce path of a rebounding ball is controlled by
several factors. When one attempts to predict the direction of the
rebound, the momentums of both the ball and the striking implement must
be considered as well as the elasticity of the two objects, the
spin of the ball, and the angle of impact. Awareness of these factors
and the ways in which they affect play have numerous and valuable
applications in sports such as handball, squash, racquetball, table
tennis, paddleball, and tennis.
Water and air are both fluids and as such are subject to many
of the same laws and principles. The fluid forces of buoyancy, drag,
and lift apply in both mediums and have considerable effect on the movements
of the human body in many circumstances. A discus sails, a baseball
curves, a volleyball “wobbles,” and a shuttlecock
drops because of contact with air currents. Sky divers and hang
gliders control their flight paths by interacting with the air currents,
whereas downhill racers, swimmers, and underwater divers streamline
their bodies to minimize the effect of fluid resistance.
If an adult female stands in shoulder-deep water and abducts
her arms as she lays her head back on the water’s surface,
most likely her feet will leave the bottom as her legs begin to
rise. At some point between the vertical and horizontal, the swimmer
will come to rest, and she will be in a motionless back float. For
this to occur, an upward force must counterbalance the weight (force) of
her body, acting vertically downward at her center of gravity. This
upward force is called buoyancy and,
according to Archimedes’ Principle, the
magnitude of this force is equal to the weight of water displaced
by the floating body. Specifically, Archimedes’ Principle
states that a solid body immersed in a
liquid is buoyed up by a force equal to the weight of the liquid
displaced. This principle explains why some objects float and
others do not, why some individuals float motionless like bobbing
corks, and why others struggle to keep their noses above water while attempting
a back float. When a body is immersed in water, it will sink until
the weight of the water it displaces equals the weight of the body.
Sinking objects never do displace enough water to equal their body
weight and eventually settle to the bottom. If such objects are
weighed underwater, they will be found to weigh less than when weighed
in air. That difference in weight equals the weight of the water
displaced and is the buoyant force acting on the immersed objects.
Even a body that floats has some part of its volume beneath the
surface and thus displaces a volume of water. The weight of the
water it displaces equals the total weight
of the floating object. Any object stops sinking when the weight
of the water it displaces equals its weight.
The ratio between the weight of an object and its volume is referred
to as density. The more weight per volume, the greater the density.
An inflated volleyball, for example, has a slightly greater volume
than a bowling ball. The bowling ball, however, weighs much more.
Because the bowling ball has more weight for its volume than does
the volleyball, it is said to have greater density.
The ratio between the density of any given object and that of
water is called specific gravity. If an object or a body has the
same density as water, or the same weight and volume ratio, it possesses a
specific gravity of 1.0. Those objects with greater density will
have a specific gravity greater than 1.0 and will sink. The bowling
ball, being very dense, will sink very quickly. Objects with a density
less than that of water will have a specific gravity less than 1.0
and will float with some part of the object or body exposed. An
example is the inflated volleyball, which is composed primarily
Human beings differ in specific gravity depending on individual
body composition. Human bone and muscle tissue both have a specific
gravity greater than water and as a result tend to sink. Fat and
air, on the other hand, have specific gravities much less than that
of water and will float. The ease with which one floats and the
floating position assumed are therefore determined by the distribution
of muscle, bone, fat, and air within the body. The specific gravity
of the various body parts differs accordingly.
Usually the legs have a high specific gravity and consequently
are the part of the body that most often sinks during the back float.
The thoracic region is the most buoyant part, having the lowest weight
for its volume. A person can increase the buoyancy of this region
by keeping the lungs inflated with air, thus increasing the ease
of floating. Some individuals have overall specific gravities greater
than 1.0. It is impossible for these people to do a motionless float
because they are “sinkers.” A practical way to
determine whether a person is a floater or a sinker is to have the person
assume the tucked jellyfish float position with lungs inflated.
If any portion of the individual’s back is on or above
the surface, the individual can learn to maintain a motionless floating position
that, even though it may be more nearly vertical than supine, is
still called a back float.
A floater has to be concerned with two forces, the downward force
of the body’s weight and the upward buoyancy of the water.
When these forces act on the body so that their resultant is zero, the
forces will be in equilibrium and the body will be in a motionless
float. The downward force acts at the center of gravity of the body,
a point somewhere in the pelvis. The buoyant force acts at the center
of buoyancy of the body, a point that varies with individuals but
is usually closer to the head than the center of gravity. If the
body were of uniform density, the center of gravity and the center
of buoyancy would coincide, but because the body has less mass toward
the head, the center of buoyancy is usually higher in the body than
the center of gravity. The center of buoyancy is the point where
the center of gravity of the volume of displaced water would be
if the water were placed in a vessel the shape and size of the floater’s
body. Because the water is of uniform density, its center of gravity
will be in the direction of the greater volume, that is, near the
chest region. If the center of gravity and center of buoyancy are
not in the same force line with each other, as shown in Figure 12.23a,
the body will rotate in the direction of the forces until the forces are
equal and opposite in line, direction, and magnitude. At this point
the floater will be in a balanced float (Figure 12.23b). Individuals
who float horizontally have the center of gravity and center of
buoyancy in the same vertical line while in the horizontal position.
These are usually individuals whose bodies contain a high percentage
of fat. Those floaters whose legs tend to drop when attempting the
back float will have a balanced position somewhere between the horizontal and
vertical at that point where the center of gravity and center of
buoyancy are in the same vertical line.
Figure 12.23Graphic Jump Location
A balanced float occurs when the gravity and the center
of buoyancy are in the same force line. G = downward
force of body weight; B = upward
force (buoyancy) of water.
The angle of the floating position with the horizontal may be
decreased by making adjustments in the position of the body segments
that move the center of gravity in closer alignment with the center
of buoyancy. Raising the arms over the head, bending the knees,
and flexing the wrists to bring the hands out of the water all contribute
to moving the center of gravity closer to the head and thus closer
to the center of buoyancy (Figure 12.23b).
The fluid resistance to movement through air or water consists
of two forces: drag and lift. The fluid flow that produces
these two resistance forces is the result of either fluid or object velocity,
which acts to produce pressure. Putting one’s hand into
a calm swimming pool will produce no fluid flow and no feeling of
pressure because there is no velocity. Moving the hand back and
forth in the pool (object velocity) or placing the hand in a fast-running-
stream (fluid velocity) produces definite pressure sensations because
of fluid flow. Similarly, a softball thrown at 30 mph on a calm
day will produce an airflow around the ball in the opposite direction
of 30 mph. If the ball were thrown into a 5-mph headwind, the airflow
velocity around the ball would be 35 mph. The magnitude of the fluid
flow is directly proportional to the fluid and object velocities.
The resistance to forward motion experienced by objects moving
through a fluid is called drag. Drag force is the result of fluid
pressure on the leading edge of the object and the amount of backward
pull produced by turbulence on the trailing edge. In fluid flow,
the layer of fluid next to the object is called the boundary layer. There will usually
be some amount of friction between the boundary layer and the object,
which will cause resistance to forward motion. This friction is
referred to as surface drag. If the
flow of fluid around an object is smooth and unbroken, it is referred
to as laminar flow. Laminar flow usually
occurs in fluids passing around a smooth surface at relatively slow
speeds. In laminar flow, the boundary layer is slowed down slightly
by surface drag but continues in a smooth, unbroken flow around
the object (Figure 12.24a). A smooth surface will produce much less
surface drag than a rough surface. New, smoother swimsuit fabrics
and the practice of shaving body hair before competition are both
examples of attempts to reduce surface drag in competitive swimming.
Figure 12.24Graphic Jump Location
Patterns of flow around an object vary with the shape
of the frontal surface. (a) Smooth, unbroken flow is laminar flow.
(b) Flow that is disrupted and creates turbulence on the trailing
edge creates drag. (c) Lift is produced when flow over one side
of the object is faster than flow over the other side.
If the surface area presented by the object is great or if the
flow velocity is high, there will be greater flow pressure on the
leading edge of the object than on the trailing edge. In this situation, the
boundary layer does not flow completely around the object. The boundary
layer separates, creating a vacuum behind the trailing edge. Fluid
rushes in to fill this vacuum, causing a back flow of fluid that
is called turbulence. Turbulence produces
a suction force backward, against the direction of motion. This
turbulence is the result of form drag.
In form drag the shape of the object is such that the fluid, moving
at a given velocity, cannot follow the contours of the object (Figure
12.24b). Drivers on interstate highways often experience turbulence
caused by form drag. When approaching a large truck from behind,
the driver of a small car may experience an agitated airflow that
tends to make the car harder to control. The driver may also feel
a pull toward the truck. Both of these are the effects of turbulence.
This turbulence might also increase as the velocity of the truck
Form drag often can be reduced by streamlining. Examples of streamlining
are common any time one desires to move easily and quickly through
air or water. The crouch position on a racing bicycle, the shape
of a race car, and the sharp bow of a boat are all examples of streamlining.
The shape of a discus is also meant to take advantage of the effects
of streamlining. The discus is tapered at both leading and trailing
edges, so the airflow does not have to make any abrupt changes in
direction. This streamlining principle will work only if the discus
is thrown so that air flows past the tapered edges. If the discus
is thrown with the flat side leading, air must make a very abrupt
change of direction. There will be increased pressure- on the leading
edge and turbulence on the trailing edge, creating a large form
drag. For this reason, streamlining makes the angle between the
long axis of the object and the direction of fluid flow very important.
This angle is often referred to as the angle
The angle of attack is also critical in producing and utilizing
the fluid force known as lift. Lift
is the result of changes in fluid pressure as the result of differences
in airflow velocities. An extremely important principle in understanding
the mechanism of lift is Bernoulli’s
Principle. Simply stated, Bernoulli determined that the pressure in a moving fluid decreases
as the speed increases. The design of an airplane wing is based
on Bernoulli’s principle of lift. The top side of an airplane
wing has a higher curve than the bottom. To avoid creating a vacuum,
airflow over the top will be at a higher velocity than the flow
across the bottom. Pressure will therefore be lower on top of the
wing. Lift will act upward, from the area of high pressure toward
the area of low pressure, causing the wing to move upward. The swimmer
uses lift in much the same way. Creating lift toward the forward
surface of the hand is one force that aids in propelling the body
forward. Lift, therefore, is the result of fluid on one side of
an object having to travel farther in the same amount of time to
avoid creating a vacuum. Lift always acts perpendicular to the fluid
flow and therefore to the drag force (Figure 12.24c).
Bernoulli’s Principle applies for moving objects passing
through a stationary fluid as well as for fluids passing stationary
objects and, in addition to explaining why airplanes can fly, it
also explains why balls with spin follow a curved path. This latter
application of Bernoulli’s Principle is called the Magnus
effect after the German physicist who first explained the phenomenon.
A ball moving through the air will also move in the direction of
least air pressure. As shown in Figure 12.25a, the ball spinning
in a clockwise direction drags around a boundary layer of air. At
the bottom of the ball this air current is moving in the same direction
as the oncoming air. At the top, the boundary air is moving in the
opposite direction. The air at the bottom is moving faster, and therefore
the pressure is reduced. The air at the top moves more slowly and
the pressure is increased. Thus the ball will move in a downward
curve in the direction of least pressure. Viewed from the side,
this would be the behavior of a ball with topspin imparted to it.
Balls with topspin drop sooner than balls with no spin. A ball with
a counterclockwise or backspin will move in an upward curve and
thus stay aloft longer than a ball with no spin (Figure 12.25b).
Balls spinning about a vertical axis have sidespin. Right spin causes
the ball to curve to the right and occurs when the forward edge
of the ball moves to the right. Left spin is the opposite.
Figure 12.25Graphic Jump Location
A spinning ball follows a curved path moving in the direction
of least pressure. (The curve is exaggerated for clarity.)
The amount of air a ball drags around with it when spinning depends
on the surface of the ball and the speed of the spin. Rough or large
surfaces, small mass, and a fast spin speed all produce a more noticeable
spin and curve deflection. The small mass of a table tennis ball,
the fuzz on a tennis ball, and the seams on a baseball all enhance
spin, an important element in each game’s strategy. The
deflection will also be more pronounced if the forward velocity
is slow. This may occur because of little force imparted to the
ball or a strong headwind. Spin on a ball may also smooth its flight
by acting as a stabilizer. Like a gyroscope, a football or discus
spinning around one axis resists spinning about another axis and
therefore is less likely to tumble through the air.