The document discusses how batting techniques in cricket have evolved over time to incorporate more attacking shots and increased risk-taking by batsmen to score runs quickly. It examines some of the key biomechanical fundamentals of batting, such as the path of the bat and angular momentum, and how coaches can optimize player development by ensuring biomechanical principles are applied appropriately within a framework focused on fundamentals. The objective is for coaches to make the act of striking a cricket ball as simple as possible for players while still allowing expression of individual batting styles.

1. Moment of inertia
From Wikipedia, the free encyclopedia
This article is about the moment of inertia of a rotating object, also termed the mass moment of inertia. For the moment of
inertia dealing with the bending of a beam, also termed the area moment of inertia, see second moment of area.
In classical mechanics, moment of inertia, also called mass moment of inertia, rotational inertia, polar moment of
inertia of mass, or the angular mass, (SI units kg·m²) is a measure of an object's resistance to changes to its rotation. It is
the inertia of a rotating body with respect to its rotation. The moment of inertia plays much the same role in rotational
dynamics as mass does in linear dynamics, describing the relationship between angular momentum and angular
velocity, torque and angular acceleration, and several other quantities. The symbolsI and sometimes J are usually used to
refer to the moment of inertia or polar moment of inertia.
While a simple scalar treatment of the moment of inertia suffices for many situations, a more advanced tensor treatment
allows the analysis of such complicated systems as spinning tops and gyroscopic motion.
The concept was introduced by Leonhard Euler in his book Theoria motus corporum solidorum seu rigidorum in 1765.[1] In
this book, he discussed the moment of inertia and many related concepts, such as the principal axis of inertia.
Contents
[hide]
1 Overview
2 Scalar moment of inertia for single body
3 Scalar moment of inertia for many bodies
o 3.1 Moment of inertia about a point
o 3.2 Moment of inertia theorems
o 3.3 Properties
o 3.4 Energy, angular momentum, torque
o 3.5 Examples
4 Moment of inertia tensor
o 4.1 Definition
o 4.2 Derivation of the tensor components
o 4.3 Reduction to scalar
5 Principal axes of inertia
o 5.1 Parallel axis theorem
o 5.2 Rotational symmetry
o 5.3 Comparison with covariance matrix
6 See also
7 Notes
8 References

2. 9 External links
[edit]Overview
The moment of inertia of an object about a given axis describes how difficult it is to change its angular motion about that
axis. Therefore, it encompasses not just how much mass the object has overall, but how far each bit of mass is from the
axis. The further out the object's mass is, the more rotational inertia the object has, and the more torque (force* distance
from axis of rotation) is required to change its rotation rate. For example, consider two hoops, A and B, made of the same
material and of equal mass. Hoop A is larger in diameter but thinner than B. It requires more effort to accelerate hoop A
(change its angular velocity) because its mass is distributed farther from its axis of rotation: mass that is farther out from that
axis must, for a given angular velocity, move more quickly than mass closer in. So in this case, hoop A has a larger moment
of inertia than hoop B.
Divers reducing their moments of inertia to increase their rates of rotation
The moment of inertia of an object can change if its shape changes. Figure skaters who begin a spin with arms outstretched
provide a striking example. By pulling in their arms, they reduce their moment of inertia, causing them to spin faster (by the
conservation of angular momentum).
The moment of inertia has two forms, a scalar form, I, (used when the axis of rotation is specified) and a more
general tensor form that does not require the axis of rotation to be specified. The scalar moment of inertia, I, (often called
simply the "moment of inertia") allows a succinct analysis of many simple problems in rotational dynamics, such as objects
rolling down inclines and the behavior of pulleys. For instance, while a block of any shape will slide down a frictionless
decline at the same rate, rolling objects may descend at different rates, depending on their moments of inertia. A hoop will
descend more slowly than a solid disk of equal mass and radius because more of its mass is located far from the axis of
rotation. However, for (more complicated) problems in which the axis of rotation can change, the scalar treatment is
inadequate, and the tensor treatment must be used (although shortcuts are possible in special situations). Examples
requiring such a treatment include gyroscopes, tops, and even satellites, all objects whose alignment can change.
The moment of inertia is also called the mass moment of inertia (especially by mechanical engineers) to avoid confusion
with the second moment of area, which is sometimes called the area moment of inertia (especially by structural engineers).
The easiest way to differentiate these quantities is through their units (kg·m² as opposed to m4). In addition, moment of
inertia should not be confused with polar moment of inertia (more specifically, polar moment of inertia of area), which is
a measure of an object's ability to resist torsion(twisting) only, although, mathematically, they are similar: if the solid for
which the moment of inertia is being calculated has uniform thickness in the direction of the rotating axis, and also has
uniform mass density, the difference between the two types of moments of inertia is a factor of mass per unit area.

3. Inertia
Inertia is the resistance of any physical object to a change in its state of motion or rest, or the tendency of an object to resist
any change in its motion. The principle of inertia is one of the fundamental principles of classical physics which are used to
describe the motion of matter and how it is affected by applied forces. Inertia comes from the Latin word, iners, meaning
idle, or lazy. Isaac Newton defined inertia as his first law in his Philosophiæ Naturalis Principia Mathematica, which states:[1]
The vis insita, or innate force of matter, is a power of resisting by which every body, as much as in it lies, endeavours to
preserve its present state, whether it be of rest or of moving uniformly forward in a straight line.
In common usage the term "inertia" may refer to an object's "amount of resistance to change in velocity" (which is quantified
by its mass), or sometimes to its momentum, depending on the context. The term "inertia" is more properly understood as
shorthand for "the principle of inertia" as described by Newton in his First Law of Motion; that an object not subject to any net
external force moves at a constant velocity. Thus an object will continue moving at its current velocityuntil some force
causes its speed or direction to change.
On the surface of the Earth inertia is often masked by the effects of friction and gravity, both of which tend to decrease the
speed of moving objects (commonly to the point of rest). This misled classical theorists such as Aristotle, who believed that
objects would move only as long as force was applied to them.

4. 2A/2B BIOMECHANICS 2
nd
ed.
www.flickr.com/photos/keithallison/4062960920/
1
©PE STUDIES REVISION SEMINARSCONTENT
Introduction to Biomechanics
•What is it?
•Benefits of Biomechanics
Types of motion in Physical Activity
•Linear
•Angular
•General
Coordination of linear motion
•Types of forces
•Kinematic Chain
•Simultaneous force summation
•Sequential force summation
Stability and Balance
•Balance
•Stability
•Centre of Gravity (COG)
•Base of Support
•Factors affecting balance and stability
2CONTENT
Newton’s laws of motion
•Force production
•Newton’s 1
st
Law of motion
•Inertia
•Newton’s 2
nd
Law of motion
•Momentum

5. •Conservation of momentum
•Impulse
•Flattening the arc
•Newton’s 3
rd
Law of motion
Projectile motion
•Trajectory of a projectile
•Factors affecting flight of a projectile
•Angle of release
•Height of release
•Velocity at take off
•Gravity
•Air resistance
•Spin 32. SEQUENTIALLY
• Where body parts are moved in sequence to produce a force.
• Generally used to produce maximal force in whole body actions such
as throwing, kicking and striking
• E.g. A baseball pitcher, striking in golf, kicking in rugby
CO ORDINATION CONTINUUM.FORCE SUMMATION
FOR MAXIMAL OR SUBMAXIMAL FORCE
www.flickr.com/photos/flash716/2579185404/ www.flickr.com/photos/martindo/3040647348/
4
©PE STUDIES REVISION SEMINARS
HomeSUCCESSFUL SUMMATION OF FORCE/MOMENTUM
•Body parts move in a sequence to generate the largest force or
acceleration possible.
•To sequentially produce maximal force effectively, the following
principles need to be applied:
1. The stronger and larger muscles of the thighs and trunk are moved first
followed by the smaller and faster muscles
2. Sequentially accelerate each body part so that optimum momentum passes
from one body part to the next.
3. Each body part should be stable so that the next body part accelerates
around a stable base to transfer momentum

6. 4. Use as many body parts as possible, so force can be applied over the
maximum possible time
5. Follow through is important to prevent deceleration of last segment and
safe dissipation of force.
6. Ensure all forces are directed towards the target
©PE STUDIES REVISION SEMINARS 5
HomeSEQUENTIAL SUMMATION OF FORCES - THROWING
Big body parts of legs and
trunk initiate movement
Wide base provides stable base
for acceleration of each
segment
Maximise number of segments
used
Follow through towards the
target to prevent deceleration
of final segment and maximise
momentum towards the target
©PE STUDIES REVISION SEMINARS 6
HomeDETERMINING THE CENTRE OF GRAVITY
• To determine ones COG, simply draw a box around the objects
outer extremities
• Then draw diagonal lines through the box, with the point of
intersection determining the objects approximate COG.
www.flickr.com/photos/dearlydeparted/3834132754/
7
©PE STUDIES REVISION SEMINARS
Home
Approximate
COGFACTORS AFFECTING BALANCE & STABILITY
Low COG =
↑ stability
High COG =
↓ stability
8

7. ©PE STUDIES REVISION SEMINARS
Home
3. THE HEIGHT OF THE COG ABOVE THE BASE OF SUPPORT
• The line of gravity or pull of gravity will always pass vertically through the
centre of an object’s mass.
• The higher the centre of gravity above the base of support, the less stable
the object is. Athletes often lower their centre of gravity by bending the
knees in order to increase their stabilityMore stable Less stable
Low COG Higher COG
Wide base of support – 4 point contact Small base of support – 2 point contact
Line of gravity in middle of support Similar line of gravity
STABILITY VARIES WITH BODY POSITION
©PE STUDIES REVISION SEMINARS 9
HomeNEWTON’S 1
ST
LAW OF MOTION
Newton’s First Law of Motion - Inertia
The size of the force required to change the state of motion of an object
depends on the mass of the object. The greater the mass of the object,
the greater the force needed to move it.
The 8kg medicine ball has a
greater inertia because of its
greater mass and therefore
requires a greater force to move it
The golf ball on the left will
remain stationary on the tee until
a force (applied by the club) is
applied to it
10
©PE STUDIES REVISION SEMINARS
Home
“A body continues in its state of rest or state of motion unless acted upon by
a force”. Newton’s Second Law of Motion – acceleration / momentum
The greater the force applied to an object, the faster the acceleration will be.
Acceleration is directly proportional to the force applied.

8. A small force applied to a ball using
a putter results in slow acceleration
A large force applied to a ball using a
driver results in faster acceleration
NEWTON’S 2
ND
LAW OF MOTION
www.flickr.com/photos/mandj98/2567621739 www.flickr.com/photos/jae_yong/679089763/
11
©PE STUDIES REVISION SEMINARS
Home
“The rate of change of acceleration to a body is proportional to the force
applied to it”.• If all other factors are constant (i.e. Speed of release, height of release,
spin, air resistance);
©PE STUDIES REVISION SEMINARS 12
1. ANGLE OF RELEASE
Home
•An angle of less than 45⁰ results in shorter horizontal distances,
shorter vertical distances and shorter flight times
•This might be useful in the following sports;
•Throwing in softball, cricket etc, stab pass in AFL
•An angle of greater than 45⁰ results in shorter horizontal
distances , greater vertical distances and longer flight times.
•This might be useful in the following sports;
•High Jump, Pole Vault, punting in American Football
www.flickr.com/photos/stuseeger/434121246/
www.flickr.com/photos/thatpicturetakr/2461107564/sizes/l/©PE STUDIES REVISION SEMINARS 13
VERTICAL MOTION
HORIZONTAL MOTION
1. ANGLE OF RELEASE
Home
Angle of release = 45⁰
•Vertical and horizontal
velocity is equal
•Max horizontal distance

9. attained
Angle of release > 45⁰
•Vertical velocity is greater
than horizontal
•↑ height and flight time
•↓horizontal distance
Angle of release < 45⁰
•Horizontal velocity is
greater than vertical
•↓ height and flight time
•↓horizontal distance

11. Q4E Case Study 10 - Cricket Batting 1
Batting is a side-on game – or at least it used t
Proposed Subject usage:
Sports Science A level & 1st/2nd yr Degre
ECB Cricket Coaches Level 1 - 4
GCSE / A-level Sports Science 2008 - Crick
National Curriculum 2008-2009 (Key Stage
3. Evaluating and improving performance. Judge how good a performance
it
AQA GCSE PE 2009 Specification
6.2 Analysis of performance
The specification will assess a candidate‟s ability to analyse performance s
Determine its strengths and weaknesses
Improve its quality and effectiveness
AQA A Level PE 2009 Specification
At AS, candidates are required to observe, analyse and evaluate performan
21.2 Observe the chosen performer in relation to the competent performa
techniques for a chosen activity
Cricket Batting 1:
The demands for International cricket batsmen have changed considerably over the past ten y
matches and one day internationals is testament to this. There is no doubt in my mind that 20
increasing the range of flamboyant strokes we see today, the reverse sweep or flick over fine l
bowler. Nobody seems to play with a straight bat anymore? Batsmen are intent on working the
pick up a quick single with a bat path that only coincides with the ball for a split second… effec
justify the risks taken?
Given that batting is such an important part of the game, it is surprising that little biomechanic
the sport. The biomechanics of the off-drive and on-drive have been found to be very similar, w
execution. Grip force patterns of top & bottom hands along with kinematic analysis of selected
however, the underlying theme from the biomechanics literature is that batting has many diffe
compare the flowing and rhythmical drives of Sachin Tendulkar, Brian Lara & Sunil Gavaskar, t
Hayden & Adam Gilchrist, or the skill and determination of an Aravinda de Silva, Ricky Ponting
becoming more apparent from the research is the degree of variation the same individual has w
look at players when they first arrive at the crease and then after scoring 50+ runs, why is this

12. A question which I have been asked on many occasions, most notably by the late Bob Woolme
very much of the opinion that, apart from teaching a few basic fundamentals, ones batting abi
primarily by the players natural flare, athletic instinct and desire to succeed. In Bob‟s opinion,
be related back to one or more of his key fundamentals. After numerous debates with Bob on t
fundamentals must be consistent throughout all batsmen: and in coaching terminology, we mu
cricket ball. So, what are these key fundamentals? Well put simply, they are made up of Dynam
the Bat and most importantly the Path of the Bat during the stroke…
Some aspects of batting cannot be supported biomechanically, however many elite players are
techniques. The objective of this article is for all coaches to ask themselves „How do you optim
the act of striking a cricket ball as simple as possible for the player?‟. I strongly believe that bio
of every batsmen, it is the responsibility of coaches to ensure that the biomechanical informati
within an appropriate time frame... The key fundamentals are discussed below;
‘Path of the Bat & Angular Momentum’ : Many of today‟s players utilize their bottom hand
during the backswing. This is a minor modification on the traditional method when batsmen wi
the top of the backlift, the face being slightly open towards second slip.
By utilizing the bottom hand as a lever, the wrists will remain close to the centre of mass, thus
the base of support (effectively making the bat lighter). If the centre of mass of the bat can be
generated is minimal, therefore, the force required by the muscles in the forearms is reduced a
action will also decrease the rotational inertia of the system. As a result the bat will travel in a
dynamic and executed faster.
The definition for ‘Rotational Inertia’ is as follows:
A rotating rigid body (for example the bat) maintains its state of uniform rotation -
unless an external TORQUE is applied or otherwise the conservation of angular mom
momentum that an object has depends on two physical quantities:
the MASS and the VELOCITY of the moving object...
Consequently, when translated into coaching terminology, this means that the cricket bat will b
cricketer‟s centre of mass. The path of the bat on the backswing and position at the top of the
action has a chain reaction in kinematics, if the arms leave the body on the backswing, this wil
counteract this action. The correct position of the hands and bat at the top of the backswing w
movement to be produced with a greater angular acceleration, it will also enable the path to be
straight bat!
Many batsmen have a distinct loop in their backswing & downswing. As a result the bat must u
from the forearms) in order to set it onto the required plane to make contact with a straight ba
compensations may go unnoticed on a good wicket, what happens if the ball nips back off the
bat are at complete odds with each other, with only a small „contact zone‟ where the two can c
path, have to wait until after the commencement of their downswing to begin to try and redire
looking to increase stroke accuracy the longer the path of the bat is in line with the ball, the m
Figure 1 is a six-image photo sequence of Michael Vaughan (MV), Mark Ramprakash (MR), Mat
match footage is taken from the Second test, West Indies vs. England – Headingley, Leeds 25t
National Cricket Academy at Loughbrough, March 06. The red line highlights the path of the to
approximately 80mph in release speed.
Each of the six-image sequences is made up of the following events:
Frame 1: The bowler is in the pre-delivery position. Note: All four of the players‟ hand
Frame 2: Trigger Movement, un-weighting of the front foot - Back foot landing of the
Frame 3: Bowler – Front Foot Contact

13. Frame 4: Point of Release (POR)
Frame 5: Ball – approximately half way down the wicket - Top of Backswing
Frame 6: Ball Impact.
Figure 1: Six-image photo sequence – Quintic v14 video ana
Traditional coaching principles generally suggest that the bat should not be taken back outside
second slip. The first 2 players in the sequence (MV & MR) illustrate during frames 1-5, how th
throughout the stroke. The position of the hands directly under their shoulders enables their w
the mass of the bat remains close to the base of support. This will decrease the „ROTATIONAL
bat also remains close to the body, allowing the mass of the bat to remain close to the base of
lighter.

14. It can be seen from the trace of the toe of the bat, that the backswing & downswing are very s
of the backswing, thus no need to re-align the bath at the start of the downswing. This also ha
swing is based on the most current ball flight information available. A controlled bat path at the
velocity alone.
The image sequences of MP & AF also highlight in frames 1-5, their wrists remaining close to t
Although the positions of their hands are directly under their shoulders, the position and path o
out towards second slip. As a result the mass of the bat goes towards the OFF-side (Frames 2
will increase the „Rotational Inertia‟ of the system. This will have the effect of making the bat fe
toe of the bat, that the backswing & downswing are two distinct traces. Both players have a lo
align the bat & shoulders at the start of the downswing. In each case their shoulders re-align t
in a continuous rhythmical manner, as in the example of Matthew Prior, demonstrates a very li
commonly described as hitting „in to out‟… The additional forces required in the forearms, uppe
inertia and re-align the bat with the path of the ball are significant, especially with today‟s heav
align early in the downswing and bring the bat down on a good plane; however, there still is an
complicate matters on a seaming wicket.
Golf is another sport where similar mechanics applies; think of the path of the club on the back
can only think of two exceptions, Jim Furyk and Eamonn Darcy, that have a considerable loop
transition. At least with golf, the ball is stationary and the path of the club through impact area
however (as with Andrew Flower & Matthew Prior) unnecessary movements of the clubhead du
pressure and as a result be inconsistent... Figure 2 highlights the trajectory of the clubhead dri
note the backswing & downswing are on a very similar path. The slight changes at the top of t
during the swing.
Figure 2: Padraig Harrington x6 image photo sequ
Quintic v14 video analysis software
Dynamic Balance – Position of Readiness? : For every action there is a reaction. If the fu
the required chaining effects of movement will not occur efficiently and effectively. The stance
about to face a delivery. It is the base to play all your shots, as the majority of coaching mater
relaxed at stance”. What is the correct stance & optimal width?
Coaching textbooks would recommend the feet approximately a foot length apart either side o
A wider base may indicate a desire to optimise stability by increasing the base of support. The
potential decline in mobility so a trade-off situation exists. In my opinion, the centre of mass of
midpoint between the feet indicating that the weight is evenly distributed on both the left & rig
evenly distributed on their heels & toes. The weight should be through your instep, or arches i
wiggle your toes, without having to change your balance. Batting is an athletic, explosive move
the best possible starting position – that of dynamic balance...
Where should the weight be positioned?
This is a great question to ask every batsman – they should be able to answer. However what
they do! Technology is needed here to give you the correct answer, force or pressure platform
accurate measurements. Traditional coaching literature would suggest the weight on the balls

15. reason being, that you can transfer quickly to either front or back foot depending on the length
the toes, this does in fact limit movement to the leg side; a classic example is people falling ov
deliveries…
As long as the batsmen is comfortable in their preferred starting position and any pre delivery
The most critical point during batting in terms of stability & balance is the position at which the
the ‘Position of Readiness’.
The batsmen does not know where the ball is going at POR, short, full, off side, straight or dow
bowlers‟ delivery action and even previous deliveries may influence the final outcome, yet until
With this in mind the batsmen needs to be in the optimal position to move and react to where
be still & eyes level at this point, but their posture needs to be alive and athletic. The easiest w
equal, both: 50% Right & 50% Left, and equally distributed by heels & toes - 50% Balls & 50%
POR, it is easy for the player to come forward, but you would require a double movement to go
weight is predominately on the front foot at POR – it‟s hard to come further forward, a double
A simple yet extremely affective way of ascertaining where a player‟s weight is at POR is to do
get comfortable by playing a number of different shots at various line & length, then simply on
watch carefully where is their body weight, are they moving forward, backwards, or falling to t
dynamically balanced at the point you fake to release the ball, they must be ready to react to w
putting themselves at a distinct disadvantage.
A recent football study undertaken by Quintic involved analysing English Premiership goalkeepe
The outcome has very similar connotations with batting. The goalkeepers, when saving a pena
the ball is struck, as they don‟t know where the ball will be targeted… If, for example, the goal
right-handed people do!) then, they were fine when diving to the right, but if they needed to d
right leg, move their centre of gravity over to the left before finally pushing off the left leg… by
effectively the distance they could cover on the left in the same time frame was significantly re
Figure 3 highlights the position of the four batsmen at the point of release. (Andrew Flower is
Where do you think the weight is distributed for each of them? Are they balanced at the point
right with the same amount of effort, or do they favour one particular movement? Are they in
Figure 3: Point of Release
In two of the above examples (MP & MV) the weight distribution is predominately on the back
the opposite having the majority of weight on the front foot, only Andrew Flower has an even
MV the next frame on the video has the left foot airborne. From looking at the above example,

16. the heels at POR, a reaction to the toe of the bat going away from the body? Chicken or egg, w
If a player has a pre delivery trigger movement there is an opportunity to move into a more dy
releases the ball. This increase in momentum can be later utilised during the stroke. You are m
start in a balanced position. However, the movement must enable the batsmen to arrive at a b
the trigger movements. Too many players are in a poor position at POR as a result of poor tim
trigger movements (they do differ during the stages of an innings), different movements to dif
inconsistency. Have a pre-delivery movement by all means, but ensure it is consistent and you
A stable base or a position of dynamic balance at POR would ensure:
Increased resistance to work the body levers against other body parts – summation o
momentum to the lighter, faster moving body parts…
Body energy transferred efficiently to the bat
Full force generation
Finally food for thought, if you increase your stability during the position of readiness, what eff
consistency?
In summary, some aspects of elite player‟s technique can not be supported biomechanically. T
coaches to ask themselves „How do you optimise the art and science of batting whilst keeping
possible for the player?‟
Biomechanical analysis is the „why‟ something happens, it is down to the skill of the coach and
the „cause and effect‟ of the any movement they observe...
Dr Paul Hurrion
(Ph.D Sports Biomechanics)
Quintic Consultancy Ltd
ECB Level IV – Biomechanics Tutor
ICC Bowling Review Group – Biomechanics Advisor
Downloads
Written Case Study
~0.8 MB