Kater's

My very first ppt

1. kater’s pendulum By charu lakshmi

2. What’s a “pendulum” anyway??? 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. Compound pendulum (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=mk 2 , 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+mL 2 The period of oscillation about p is given by T 2 =4 Π 2 (I+mL 2 )/Lgm T 2 =4 Π 2 (k 2 +L 2 )/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 . Kater’s pendulum

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. Kater’s approach

11. Applying formula for period of motion at both the pivots and comparing it ,we get 4 Π 2 /g=1/2[ (Ta 2 + Tb 2 )/La+Lb +(Ta 2 -Tb 2 )/ 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=4 Π 2 L /T 2

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. Procedure

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=4 Π 2 L/To 2

15. T he End

16. If you think ,you can!!!!!