Which formula is used in determining modulus of rigidity by torsional pendulum?

Torsion Pendulum Principle I = Mass moment of inertia of the rotating system about the longitudinal axis of wire. L = Length of the wire between its grips. N = Modulus of rigidity (Shear modulus).

What is the formula of torsional pendulum?

The length between the point of rotation and the center of mass is L. The period of a torsional pendulum T=2π√Iκ T = 2 π I κ can be found if the moment of inertia and torsion constant are known.

What is the principle of torsional pendulum?

A torsional pendulum, or torsional oscillator, consists of a disk-like mass suspended from a thin rod or wire. When the mass is twisted about the axis of the wire, the wire exerts a torque on the mass, tending to rotate it back to its original position.

Can we determine rigidity modulus of the wire using irregular shaped body in torsional pendulum experiment?

It is possible to calculate the rigidity modulus of the material of the wire using the torsion pendulum experiment.

What is the unit of modulus of rigidity?

pascal (Pa)
The SI unit of Modulus of rigidity is pascal (Pa). Shearing Stress is the ratio of the force applied on the body to the area on which the force is applied. Shearing strain is the ratio of the transverse displacement of the surface of the body to the initial length of the body.

How do you calculate modulus of rigidity?

Modulus of rigidity or shear modulus is the rate of change of unit shear stress with respect to unit shear strain for the condition of pure shear within the proportional limit. Modulus of rigidity formula is G = E/(2(1+v)), and modulus of rigidity is G, elastic modulus is E and Poisson’s ratio is v in the formula.

What forces are acting on a pendulum?

The forces acting on the bob of a pendulum are its weight and the tension of the string. It is useful to analyze the pendulum in the radial/tangential coordinate system. The tension lies completely in the radial direction and the weight must be broken into components.

How do you find the angle of a pendulum?

The formula is t = 2 π √ l / g . This formula provides good values for angles up to α ≤ 5°. The larger the angle, the more inaccurate this estimation will become.

What is the uses of torsional pendulum?

Similar to the simple pendulum, so long as the angular displacement is small (which means the motion is SHM) the period is independent of the displacement. Torsional pendulums are also used as a time keeping devices , as in for example, the mechanical wristwatch .

What is called torsion?

1 : the twisting or wrenching of a body by the exertion of forces tending to turn one end or part about a longitudinal axis while the other is held fast or turned in the opposite direction also : the state of being twisted. 2 : the twisting of a bodily organ or part on its own axis.

What is the role of rigidity modulus in torsion pendulum?

A torsion pendulum is an oscillator for which the restoring force is torsion. Rigidity modulus or shear modulus is the ratio of shear stress to the displacement per unit sample length. This effect is used to determine the rigidity modulus of the suspended wire.

What do you mean torsional rigidity?

The applied torque needed to produce a unit angle of twist in a circular elastic material; a measure of a body’s resistance to torsion. From: torsional rigidity in The Oxford Dictionary of Sports Science & Medicine » Subjects: Medicine and health — Clinical Medicine.

How is rigidity modulus measured with torsion pendulum?

Part 1: Determination of Rigidity modulus using Torsion pendulum alone. The radius of the suspension wire is measured using a screw gauge. The length of the suspension wire is adjusted to suitable values. The wire for the test is tightened at its bottom to the disc and its top to the bracket.

How is the oscillation of a torsional pendulum defined?

Torsional oscillation It is the periodic oscillation produced by twisting the wire 2. Torsional pendulum A body suspended from a rigid support by means of a thin elastic wire is called a torsional pendulum 3. Rigidity modulus Rigidity modulus is defined as ratio of shearing stress to shearing strain 4. Moment of Inertia

What is the rigidity modulus of a wire?

Modulus of Rigidity is the coefficient of elasticity of wire for a shearing force. In simple words, rigidity modulus of a metal wire is a measurement of the capability of a material to resist deformation when external tangential (parallel to the surface) force is applied to the metal wire. Fig 1: Torsion Pendulum Test Apparatus

How to measure the inertia of a pendulum?

1. To measure the time period of the torsional pendulum 2. To calculate the moment of inertia of the disc 3. To measure the radius of the wire using screw gauge 4. To determine the rigidity modulus of the wire using the formula APPARATUS REQUIRED