torsional pendulum

 Torsional Pendulum:

 In torsional pendulum, an extended body is suspended by a light thread or wire. The body is rotated through an angle about the axis of rotation.

The wire remains vertical during this motion but twist Ө  is produced in the wire. The twisted wire exerts a restoring torque on the body, which is directly proportional to the angle of twist 

                                 τ α –θ

                                 τ = -k θ   

where k is the proportionality constant called torsional constant of the wire.

If I be the moment of inertia of the body about the vertical axis, then the angular acceleration of the body will be -------

     As we know,            τ = I α

                                     α = τ/I
                                     α = –kθ/I
                                     α = –ω2θ
Therefore,                    ω2 = k/I

                                             ω = (k/I)^1/2    

     As we know,                   T = 2π/ω   

                                             T = 2π(I/k)^1/2     

                                                                      https://youtu.be/O3D2belxKBs