Lab 2 Torsional pendulum Goal This experiment is designed for a review of the rotation of rigid body Related topics Rotational motion, Oscillatory motion, Elasticity Introduction A torsional pendulum, or torsional oscillator, consists usually of a disk-like mass suspended from a thin rod or wire(see Fig. 1). 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 will measure the moment of inertia of several different shaped objects. As comparison, these moment of inertia can also be calculated theoretically. We can also verify the parallel axis theorem Given that the moment of inertia of one object is known, we can determine the torsional constant Fig. I Schematic diagram of a torsional pendulum This experiment is based on the torsional simple harmonic oscillation with the analogue of displacement replaced by angular displacement e, force by torque M, and the spring constant by torsional constant K. For a given small twist 6(sufficiently small), the experienced reaction is given by M=-K8 (1) This is just like the Hooke's law for the springs. If a mass with moment of inertia / is attached to the rod, the torque will give the mass an angular acceleration a according to m=a=/ get the following d-e K 6 Hence on solving this second order differential equation we get 8=Acos(t+o)7 Lab 2 Torsional pendulum Goal This experiment is designed for a review of the rotation of rigid body Related topics Rotational motion, Oscillatory motion, Elasticity Introduction A torsional pendulum, or torsional oscillator, consists usually of a disk-like mass suspended from a thin rod or wire (see Fig. 1). 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 will measure the moment of inertia of several different shaped objects. As comparison, these moment of inertia can also be calculated theoretically. We can also verify the parallel axis theorem. Given that the moment of inertia of one object is known, we can determine the torsional constant K. Fig. 1 Schematic diagram of a torsional pendulum This experiment is based on the torsional simple harmonic oscillation with the analogue of displacement replaced by angular displacement , force by torque M, and the spring constant by torsional constant K. For a given small twist  (sufficiently small), the experienced reaction is given by M K    (1) 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  according to 2 2 d M I I dt      Then we get the following equation: 2 2 d θ K dt I    (2) Hence on solving this second order differential equation we get:      A t cos( ) (3)