My very first ppt

2. Pendulum in Latin means hanging
Something hanging from a fixed point which,
when pulled back and released, is free to swing
down by force of gravity and then out and up
because of its inertia.
Inertia: means that bodies in motion, will stay in
motion; bodies at rest, will stay at rest, unless
acted on by an outside force.

3.  it can be used to provide accurate
 it can be used to measure (the
acceleration due to gravity) which is
important in determining the shape of the
earth and the distribution of materials
within it (the science of geodesy)
 And also it can be used to show that

4. Like the earth was flat. many theories came
up from scientists like Copernicus
,Aristarchus etc but they were termed as
“nuts”
then there was Newton's inertia and stuff,
which induced ideas in dynamic men of that
age :P

5.  The pendulum has long been a favorite
instrument for measuring the acceleration of
gravity
 But the determination of “g” suffers from
complications , if we want high precision.
 Such as , when the length of a pendulum
increases, it is increasingly susceptible to
noises, both from surrounding air and also
from the support which is never completely
inertial.

6. “Compound
pendulum” eh??
As we try to modify simple pendulum, to
improve its performance ,it becomes
compound!!!!
Consider an extended body of mass with a hole drilled though it.
Suppose that the body is suspended from a fixed peg,
which passes through the hole, such that it is free to swing from side to side,
This setup is known as a compound pendulum.

7. (Taking d as L)

8.  Suppose p is the pivot axis of the compound
pendulum and G is the centre of gravity.
Its moment of inertia I about an axis through G
parallel to p is I=mk2 , where m is the pendulum’s
mass and k is radius of gyration.
 By the parallel axis theorem ,the moment of inertia
about p is I+mL2
 The period of oscillation about p is given by
T2=4Π2(I+mL2)/Lgm
T2=4Π2(k2+L2)/Lg

9.  Kater’s pendulum is a compound pendulum, in
which the pendulum's centre of gravity don't have
to be determined, allowing greater accuracy.

10.  Kater knew that for the pendulum equation to be
precise he needed to know the pendulum’s I. This
amounts to the knowledge of radius of gyration. it is
this radius that is hard to measure precisely since it
depends on the distribution of the mass in the
pendulum. so Kater decided to build a reversible
pendulum.
 It has pivots on each end ,with two movable masses
.They are in line the with centre of mass. The value of
the period of oscillation is different in both the ends
.if the movable weight is adjusted until the periods
for both orientations of pendulum becomes equal, we
get our special result “g”
 When this case gets satisfied ,Kater's pendulum
becomes equivalent to a simple pendulum.

11.  Applying formula for period of motion at both
the pivots and comparing it ,we get
4Π2/g=1/2[ (Ta2 + Tb2)/La+Lb +(Ta2-Tb2)/ La –Lb]
This equation is called Bessel's equation.
if Ta and Tb are nearly equal ,the approximate value of La- Lb
can be considered.
if Ta=Tb, then
g=4Π2 L /T2

12.  Keep the knife edges at a distance L cm apart;
 Keep the bob say d=5 cm apart from the
knife edges.Suspend the pendulum along ka,
note down the period of oscillation Ta , lll’y
for Tb.
 Repeat the experiment for d=10, plot the
graph of time Ta and Tb against d.the
intercept on the abcissa is do.

13.  Now keep the distance d=do between bob
and nearest knife edge.
 Find Ta and Tb for 100 oscillations about ka
and kb.
 Find the centre of gravity of the pendulum
 La +Lb =L; and La is the distance from cog to
ka and Lb is the distance from cog to kb.
 Find g using the formula .

14. Part -3
 Keep the distance btw bob and knife edge as
d=do(+/- )0.5
 Note down Ta and Tb ,plot the graph T
against d.
 To is the value of the intercept on y axis
 Substituting the value of To in
g=4Π2 L/To2