### cue ball - 2010SMTPSec3

```Teo Jim Yang
3O3 26
 Introduction
to Cue Sports
 Physics Concepts Involved in Cue Sports
 Before Collision: Hitting the Cue Ball
 During Collision: When the Cue Ball hits the
Object Ball
 After Collision: The Motion Path of the Cue Ball
 Kicks and Banks: How to pot the Object Balls
efficiently
 Using
a cue stick, the objective is to
strike the cue ball to hit other billiard
balls into one of six pockets or pots on a
billiard table
 Generally known as billiards, but has
many sub-categories including:
• Snooker
• Pool (pocket billiards)
• Carom Billiards
 Kinematics and
• Velocity
• Acceleration
• Momentum
• Impulse
 Friction
 Angular
Dynamics
Momentum (or Spin)
The physics of billiards is a lot similar to
the way light rays behave!
 Velocity
(displacement/time)
• The speed at which the balls move across the
table
• Dependent on the force exerted by the cue stick
 Acceleration
(displacement/velocity)
• The rate of change in speed
• Speeds up and slows down due to human force
(via the cue stick) and frictional force
respectively

Momentum (mass x velocity)
• When one ball hits another, the first will impart velocity to
the second through momentum
• When the cue ball hits another ball, the other ball will
move with similar velocity, but the cue ball will slow, if not
halt altogether
• The total momentum of the system, before, during, and
after the hit remains the same

Impulse (mass x change in velocity)
• Change in momentum of an object over time
• Describes the collision and transference of velocity from
ball to ball
A
billiard table is made to be as flat as
possible, with few surface imperfections
• Insures that game play is predictable and consistent
between tables
 Table material: Felt
• Slows down the movement of the balls considerably
• As the ball rolls across the table, the fibres in the felt
gently push on the surface of the ball, producing
spin
Before Collision
 Mass
x Directional Velocity
 Occurs when the cue ball is hit off-center
• Just like when a light ray enters a medium, it will
refract unless it enters perpendicular to the medium
3
types of billiards spin
• Follow
• Draw
• English
 It
is a form of momentum, thus:
• Can be imparted from one ball to another
Follow
 Caused by hitting the ball above the
horizontal plane
Draw
 Caused by hitting below the horizontal
plane
English
 Caused by hitting the ball somewhere on
either side of the vertical plane
Center ball (hitting it dead center)
 It slides for a short distance before
rolling
 The harder the ball is hit, the farther it
slides before the ball is rolling
Draw (below center)
 First the ball rotates backward
 This rotation slows as the ball slides, and
then the ball rolls forward as it does on
other shots
 The harder the ball is hit, the farther the ball
will travel with this backward spin
 If the cue ball hits another ball solidly when
it still is spinning backwards, this backward
spin will make it come back toward you
after the collision
 Cue ball rotates forward
 If the cue ball then hits another ball, it
will roll forward after the collision
 Stop Shot (cue ball stops after collision)
• The cue ball slides to the object ball and stops dead
as the object ball shoots ahead because of the
collision
• Can be accomplished using center ball or draw
 Jump
Shot (cue ball ‘jumps’ over one billiard
ball to hit another)
• Impart extreme spin on the cue ball or elevate
greatly the cue stick
• Jump Shot Example
• A shorter jump cue makes the jump higher and
more dramatic
• The type and thickness of the cloth may also be a
factor in how high the cue ball jumps
 The
area of the cue ball where it is struck
so that no friction force develops
between the ball and the table
 Pure rolling of the ball will always result
after impact
During Collision
 When
two billiard balls collide the
collision is nearly elastic
• An elastic collision is one in which the kinetic
energy of the system is conserved before and
after impact
 Conservation
of Energy
• Energy cannot be created nor destroyed; only
transferred from one object to another
• KE is thus transferred from ball-to-ball during
collisions
 In
the simplest case,
when a cue ball hits an
object ball in a straight
line, the resulting path of
the object ball will be
along the line that
connects the center of
the two balls at contact

90 Degree Rule: The
resulting path of the cue ball
will be perpendicular (90
degrees) to that line
When the cue ball hits the
object ball at an angle, the 90
Degree Rule still applies
 The line L1 is drawn at a
tangent to both balls at the
point of contact

• L1 is perpendicular to the line
passing through the centre of
the two balls and the contact
point CP
• L1also makes an angle θ with the
vertical, and the line passing
through the centre of the balls
makes an angle θ with the
horizontal.
After impact at CP, ball B
moves in the direction of the
line joining the centre of the
two balls (blue line)
 Force delivered by ball A to
ball B acts normal to the
surface of ball B, Thus, ball B
moves in the direction of this
force
 After impact, ball A moves in
a direction perpendicular to
the direction of ball B

 Using
a vector diagram of
the blue, green and red
lines (the displacement of
the balls before and after
collision), the relationship
between the forces can be
easily seen:
 However, the
resultant direction of the
object ball after collision usually deviates
slightly due to frictional force with the
table
 This deviation is known as throw
 This is common when the cue ball is
struck English or when the cue ball
strikes the object ball at an angle
 When
the cue ball is given side English,
as in the diagram, it spins anti-clockwise
 Similar to the movement of gears, the red
and yellow balls spin in the opposite
 This causes the yellow ball to be ‘thrown’
to the right
After Collision
 If
the cue ball had center ball during
collision, it should move at a right angle
to the path of the object ball
(perpendicular)
 With follow, the cue ball will curve
forward
 With draw, the cue ball will curve
backward
Kicks and Banks
 Donald
 The
Duck and Billiards
video shows how the paths of the
balls can be perfected by using concepts
of physics and mathematics
A
bank shot is when you drive an object
ball into the rail (side of the table) and
then into a pocket, somewhere on the
other side of the table
 A kick shot is when you drive the cue ball
into the rail, and then into the object ball
 This is a lot like the reflection of a light
ray off a mirror
 There
are many ways to accomplish kick
and bank shots
• Bank Shot
• Kick Shot
 By
using physics concepts, cue sports
can be more easily understood and
picked up
 On the other hand, using cue sports is
also a fun way to understand physics
concepts better
 http://www.klsgametables.com/english.htm
l
 http://www.pool-billiardsgame.com/billiard-drills.html
 http://www.trickshottim.com/learn/poolphysics.html
 http://www.real-world-physicsproblems.com/physics-of-billiards.html
 http://www.jimloy.com/billiard/phys.htm
 http://www.suite101.com/content/billiardsand-angular-momentum-a24691
 http://www.billiardworld.com/index.html
```