Torision ppt for Rigidity Modulus of a simple Pendulum .pptx

Torsion Basics Notes

1. GOOD AFTERNOON

2. . Rigidity Modulus of The Suspension Wire of A Torsion Pendulum

3. Torsion pendulum   A torsional pendulum consists of a disk (or some other object) suspended from a wire, which is then twisted and released, resulting in an oscillatory motion

4. The first torsion pendulum was developed by Robert Leslie in 1793.

5. What is modulus of rigidity   Defined as shearing stress to shearing strain. It is also known as Modulus of Rigidity.   S.I. Unit:  N/m 2  or Pascal(Pa)

6. AIM To determine the rigidity modulus of the suspension wire using torsion pendulum

7. Apparatus  

8. Torsion Pendulum

9.  Stop watch

10. Meter scale  

11. Two identical cylindrical masses

12. Important Formulae used are  

13. The period of oscillation of torsion pendulum (T)     I=moment of inertia of the  suspended body  C=couple/unit twist

14. Moment of inertia Moment of inertia can be defined as a quantity that expresses a body’s tendency to resist angular acceleration, which is equal to the sum of the products of the mass of each particle in the body with the square of its distance from the axis of rotation.  Its formula is given by      I = L/ω                I denotes the inertia                                                                               L denotes the angular momentum                                                                               ω denotes the angular velocity).   Angular acceleration     The angular acceleration is  the time rate of change of the angular velocity   and expressed in radians per second per second.   Angular velocity  is a vector measure of rotation rate, that refers to how fast an object rotates or revolves relative to another point

15. Moment of inertia of the given disc (I )   T ,T 1 ,T 2 - are the periods of torsional oscillation   d1&d2 -  Distances 

16. Rigidity Modulus The modulus of rigidity is defined as the ratio of tangential stress to shear strain

17.  The rigidity modulus of the suspension wire (n)

18. The Simulation and  Procedure  part  

19. Tabular Column

20. General use Torsion pendulums are often used for time-keeping purposes. For instance, the balance wheel in a mechanical wristwatch is a torsion pendulum in which the restoring torque is provided by a coiled spring.

21. Applications of Torsional Pendulum: 1. The working of  " Torsion pendulum clocks " ( shortly torsion clocks or pendulum clocks), is based on torsional oscillation. 2. The freely decaying oscillation of  Torsion pendulum in medium(like polymers),helps to determine their characteristic properties. 3. New researches, promising the determination of frictional forces between solid surfaces and flowing liquid environments using forced torsion pendulums.

22. Conclusion We conclude that when a torsion pendulum is perturbed from its equilibrium state (i.e., θ  = 0 ), it executes torsional oscillations about this state at a fixed frequency, , which depends only on the torque constant of the wire and the moment of inertia of the disk.  Note, in particular, that the frequency is independent of the amplitude of the oscillation

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