A uniform disk of radius r= 0.6 m and mass M = 2.5 kg is freely suspended from a horizontal pivot located a radial distance d = 0.30 m from its centre . Find the angular frequency of small amplitude oscillations of the disk .

A uniform disk of radius r= 0.6 m and mass M = 2.5 kg is freely suspen

1.	A uniform disk of radius r= 0.6 m and mass M = 2.5 kg is freely suspended from a horizontal pivot located a radial distance d = 0.30 m from its centre . Find the angular frequency of small amplitude oscillations of the disk .
Answer» Solution :The MOMENT of inertia of the DISK about a PERPENDICULAR axis PASSING through its centre is `I=1/2mr^(2)` Form the PARALLEL axis theorem , the moment of inertia of the disk about the pivot point is `I'=I+Md^(2)=(2.5xx0.6xx0.6)/(2)+2.5xx0.30xx0.30` `=(0.9)/(2)+0.225` `=0.45+0.225` `=0.675kgm^(2)` The angular frequency of small amplitude oscillations of a compound pendulum is given by `omega =sqrt((Mgd)/(I'))=sqrt((2.5xx9.8xx0.30)/(0.675))` `=sqrt((7.35)/(0.675))=sqrt((0.675)/(10.9))=3.3"rad"/s`