Consider a uniform circular disk of radius R = 5 cm, pivoted smoothly at its centre of mass. As shown in the below figure, a spring of constant K = 5 N/s is connected to it. If the mass of the disk is m = 2 kg, then the angular frequency of torsional oscillations of the disc when it is given a small disturbance is `omega` rad /s. Find w=? (Take `sqrt5 = 2.23` )

Answer

2.23

Explanation

If disc is twisted clockwise for a small angle `theta` deformation in spring (x) `= "R" theta`
`implies F_s = kx =k("R"theta)`
`tau_("res") = -F_sR`
= `-kR^2 theta ……(i)`
Also `tau = I_c alpha ....(ii)`
From (i) & (ii)
`implies alpha=(kR^2 theta)/I_c`
`-(2k)/mtheta...[ :. I_c =(mR^2)/2]`
Comparing with standard equation ,
`omega^2 theta = (-2k)/m theta`
`:. omega=sqrt((2k)/m)`
`=sqrt((2xx5)/2)`
`:. omega = 2.23` rad/s