Aim : To determine the moment of inertia of the given irregular (Iα & Iβ) body and also determine the rigidity modulus (η )of the given wire using a torsional pendulum.
Apparatus: Rectangular plate, circular plate, irregular body, set of weights, rough balance, stand with clamp, steel wire fixed between chucknuts, meter scale, stop clock, etc.
Formula :
η=(8 π l)/r^4 (I/T^2 )_mean N/m2
where, η is the rigidity modulos of suspended wire (N/m2)
I is the moment of inertia of suspended wire (kg-m2)
l is length of wire between two chuck nuts (m)
r is radius of the wire (m)
T is the time period (sec)
Procedure:
The mass of the given rectangular and circular plates are determined by rough balance. The length and breadth of the rectangular plate is measured using meter scale and also the circumference C of the circular plate are found by using meter scale. The moment of inertia values of two bodies about the respective axes are evaluated by using the corresponding equations listed in the tabular column.
The two ends of the wire are fixed to chucknuts and one end being fixed at the stand on the other is used to suspend the given value. The length of the wire between two chucknuts is measured. The wire is twisted so that it executes torsional oscillations. The time taken by the each body to make 20 oscillations is noted. To calculate the time periode (T) for each oscillation, time t1 & t2 of rectangular & circular bodies are calculated. The moment of inertia is calculated using the formula given in tabular column and the value of ( I / T2 ) and mean value of is noted.
Determination of moment of inertia of irregular body :
The given irregular body is suspended to the experimental wire. The time taken to execute for 20 oscillations about an axis perpendicular to the plane. From which the value of time periode (T) and hence T2 is calculated. The moment of inertia Iα of the body about the same axis is found by evaluating (I/T^2 )_mean×T^2 . Similarly the moment of inertia of the body Iβ and parallel to its plane is also found out.
Determination of rigidity modulus η of the suspension wire material :
The length between chucknuts (l) is evaluated. Finally, The rigidity modulus  is evaluated using the given formula.