which of the wire oscillated faser in torsional pendulum
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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.
1. Introduction
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. If twisted and released, the mass will oscillate back
and forth, executing simple harmonic motion. This is the angular version of
the bouncing mass hanging from a spring. This gives us an idea of moment
of inertia. We try to calculate the moment of intertia of a ring given the
moment of a disc. We can also verify the perpendicular axis theorem and
compare it with theoretically calculated values.
The working is based on the torsional simple harmonic oscillation with
the analogue of displacement replaced by Angular displacement θ, Force by
Torque τ and the dpring constant by torsinal constant κ. For a given small
twist θ (suffciently small), the experienced reaction is given by
τ = −κθ
This is just like the Hooke’s law for the springs. If a mass with moment
of inertia I is attached to the rod, the torque will give the mass an angular
acceleration α according to τ = I
d
2θ
dt2 . Hence we get the relation
d
2
θ
dt2
= −
κ
I
θ
. Hence on solving this second order differential equation we get
ω =
r
κ
I
.Hence we have
T = 2π
r
Il
κ
1
2 RAVITEJ UPPU
where l is the length of suspension. This is our governing equation of the
experiment.