enjoy the physics of cricket

1. PHYSICS IN THE WORLD OF
CRICKET
Projectile motion momentum magnus effect numericals

2. CRICKET BALL : A PROJECTILE
PROJECTILE
• Projectile is the name given to a body thrown with some initial velocity, and then
allowed to move in two dimensions under the action of gravity alone, without being
propelled by any engine or fuel. The path followed by a projectile is called its trajectory.

3. EXAMPLES OF PROJECTILES
• A cricket ball hit by a bat.
• A javelin or hammer thrown by an athlete.
• A bullet fired from a rifle.
• A piece of stone thrown in any direction.

4. ASSUMPTIONS IN PROJECTILE MOTION
1. There is no frictional resistance of air.
• 2. The effect due to rotation of earth and curvature of the earth is
negligible.
• 3.The acceleration due to gravity is constant in magnitude and direction at
all points of the motion of projectile.

5. MAXIMUM HORIZONTAL RANGE.
we note that for a given speed u of the
object, the value of horizontal range
depends upon angle of projection as g is
constant at a place. Therefore horizontal
range R will be maximum if
Sin 2θ = maximum = 1
= sin 90°
Or 2θ =90° or θ =45°

6. HEAVY OR LIGHT BAT
LAW OF CONSERVATION OF MOMENTUM
• Momentum is total quantity of motion possessed by body
• It is product of mass and velocity
• If the Bat is heavy, then even a slight swing can provide enough momentum to ball
to cross the boundary. Whereas if bat is light it can swing 10% faster and impart same
momentum to ball. Having a heavy bat gives more advantage as it proves to be more
powerful. If all bats are swung at same medium speed. Heavy & light terms are relative
with respect to age. Therefore one must use a bat as heavy as one feels comfortable to
swing.

7. WHY A CRICKETER LOWERS HIS HANDS WHILE CATCHINGA BALL?
Impulse It is effect of force acting for a
short interval of time.
According to Newton’s 2nd law
Rate of change of momentum = Force
applied.
If time period dt is
increased than Impact force decreases.

8. WHY A CRICKETER LOWERS HIS HANDS WHILE CATCHING A BALL
• If suppose a 0.16 kg cricket ball hits a bat at 100 km/hr and then comes off the
bat at 100 km/hr in 0.001 sec. The average force on ball is 8800 N which is
enough to lift 880 kg of mass off the ground. That is why it hurts to get struck by
ball. Therefore while catching cricketer lowers his hands to increase time interval
of change in momentum thereby impact force reduces.

9. SPIN
1. The first axis is vertical pointing
towards sky.
2. A ball that spins about vertical axis
will deflect in air to left or right and
there is no deflection when it bounces.

10. SPIN
The second axis points along the pitch
towards the batsman when cricket ball
spins or about this axis.
It does not deflect in air, but deflects
sharply towards left or right after the
bounce.
By dropping the spinning ball vertically we
can notice this change.

11. The third axis is across or perpendicular
to pitch. Spinning the ball about third axis
results in top spin or back spin.
A Top spin ball dives towards the pitch
faster and bounces at reduced angle since
it kicks forward when it bounces.
A back spin ball kicks up after it
bounces, causing the ball to slow down.
The actual result depends on both the
amount of spin and angle of incidence.
SPIN

12. SWING
• Ball surface
• If during the play one side of the ball roughs up and other
side remains smooth. Then swing occurs
• Swing is swerving of cricket ball towards left or right as it
moves through air. This happens when ball spins about its
vertical axis or because it spins about an axis perpendicular to
the seam.

13. SWING
The fast bowlers swing the ball by making the
seam inclined at angle of 15° to 25° to the
direction that the ball is headed such that the
smooth portion of ball is above & in front.
In this way the air flows smoothly around the
smooth half but it becomes turbulent on other
side as it has to flow past the seam.

14. SWING
• The turbulent air is at higher velocity. Therefore according to
Bernoulli’s theorem the pressure on these side (rough)
decreases than on smooth flowing air therefore the ball gets
pushed sideways.
• This is also the Magnus effect. This sideway swing force is
maximum when speed of ball is around 100 km/hr. But it
speed of ball increases.
• The reverse swing occurs because the flow of air over
smooth surface becomes turbulent. The effect can occur at
low speeds if rough end side is put forward.

15. SWING
• Other factors: affecting swing are the atmospheric
pressure: - Due to evaporation of ground moisture. The
water vapor content of air over pitch increases. This
increases the partial pressure and thereby air pressure
therefore as match progress the fast bowlers will be able
to get more swing if they manage roughness/shine factor
well.

16. OUTSWING AND INSWING
(1)Holding the ball for an out
swinger with shiny/wet side on
right side
The ball initially moves out in
the air and comes back to the
batsman sharply. Usually, a
batsman can be out by leg
before as the tends to play
along wrong line.

17. OUTSWING AND INSWING
• (2) Holding the ball for an in
swinger, with shiny side on the left
side
• The ball initially moves
towards the batsman and at last
moment darts away from the
batsman. A batsman can be caught
behind the wickets and sometimes
bowled.

18. SHINING THE BALL
• Most of us have watched cricketers rub the ball near
their crotch almost every time they have the ball. The
question is why?
• Shining the ball helps the ball to swing. As the game
goes on the ball receives consistent impact on the surface.
But one side of ball is emphasized and taken care of by the
bowlers. What you should end up with is ball distinctly shiny
on one side and rough on other. If projected, a bowler can
chose which direction he wants the ball to swing. If rough
side is on left side the ball will swing towards left and if it is
on right side it will swing towards right. Aerodynamics,

19. STREAMLINE ANDTURBULENTFLOW
Streamline flow of a liquid is that flow in which every particle of the
liquid follows exactly the path of its preceding particle and has the
same velocity in magnitude and direction as that of its preceding
particle while crossing through that point.
Turbulent flow
• When a liquid moves with a velocity greater than its critical
velocity, the motion the particles of liquid becomes disorderly or
irregular. Such a flow is called turbulent flow.

20. CURVEDMOTION OF SPINNING BALL (MAGNUS EFFECT)
• When a spinning ball is thrown, it deviates from its usual path in flight. This is due
to magnus effect..
• If the ball is spinning as well as moving linearly, the streamlines at the top of ball
due to two types of motion are opposed to each other and those below are in the same
direction. As a result of it, the velocity of air flow is greater below than above the ball.
Now, according to Bernoulli’s principle, the pressure on the upper side of the ball
becomes more than the pressure on the lower side of ball. Due to it, a resultant force F
acts upon the ball at right angle to the linear motion in the downward direction,
resulting the ball to move along a curved path. This dynamic force due to spinning of ball
is called Magnus effect.

21. SIX OR FOUR?
• S2) Sachin Tendulkar, the little master is
batting at the crease. Glenn Mc Grath,
delivers a short–pitched ball and
Tendulkar pulls it. The boundary is
unguarded. Tendulkar strikes the ball at
an angle of projection of 15° with a
velocity of 35m/s. Decide whether the
ball will cross the boundary for a sixer or
it will fetch only a four.

22. 1Sol: Initial Velocity of the ball, u = 10 m/s.
Retardation of the ball due to friction, a = 1.25 m/s2
Radius of the circular field = 50m
Final velocity oif the ball v = 0, as it come to rest due to retardation.
Now, we have to find whether the ball crossed the boundary or no. The formula
connected with u, v, a and S is v2 – u2 = 2aS
0 – (10)2 = 2 × (1.25) ×S
But the radius of the field is 50m, and the ball is stopped at a distance of 40m.
Therefore the boundary is saved and Australia will not get the boundary.
mS 40
25.12
100
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 mS 40
25.12
100
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