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
Slide 3
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
Slide 4
Kinematics and Dynamics Velocity Acceleration Momentum Impulse
Friction Angular Momentum (or Spin) The physics of billiards is a
lot similar to the way light rays behave!
Slide 5
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
Slide 6
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
Slide 7
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
Slide 8
Before Collision
Slide 9
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
Slide 10
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
Slide 11
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
Slide 12
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
Slide 13
Follow (above center) Cue ball rotates forward If the cue ball
then hits another ball, it will roll forward after the
collision
Slide 14
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
Slide 15
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
Slide 16
During Collision
Slide 17
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
Slide 18
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
Slide 19
When the cue ball hits the object ball at an angle, the 90
Degree Rule still applies The line L 1 is drawn at a tangent to
both balls at the point of contact L 1 is perpendicular to the line
passing through the centre of the two balls and the contact point
CP L 1 also makes an angle with the vertical, and the line passing
through the centre of the balls makes an angle with the
horizontal.
Slide 20
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
Slide 21
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:
Slide 22
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
Slide 23
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 direction to the adjacent ball
This causes the yellow ball to be thrown to the right
Slide 24
After Collision
Slide 25
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
Slide 26
Kicks and Banks
Slide 27
Donald Duck and Billiards Donald Duck and Billiards The video
shows how the paths of the balls can be perfected by using concepts
of physics and mathematics
Slide 28
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
Slide 29
There are many ways to accomplish kick and bank shots Bank Shot
Kick Shot
Slide 30
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