An Angular Simple Harmonic Oscillator
shows an angular version of a simple harmonic oscillator; the element of springiness or elasticity is associated with the twisting of a suspension wire than the extension and compression of a spring as we previously had. The devic called a torsion pendulum, with torsion referring to the twisting.
If we rotate the disk in by some angular displacement e from its position (where the reference line is at e = 0) and release it, it will oscillate at that position in angular simple harmonic motion. Rotating the disk through angle e in either direction Introduces a restoring torque given by Here K (Greek kappa) is a constant, called the torsion constant, that depends the length, diameter, and material of the suspension wire Comparison of with leads us to suspect that the angular form of Hooke’s law, and that we can transform which the period of linear SHM, into an equation for the period of angular SHM replace the spring constant k in with its equivalent, the constant and we replace the mass m in with its equivalent, the inertial of the oscillating disk. These replacements lead to
which is the correct equation for the period of an angular simple harmonic oscillator or torsion pendulum.