Damaged clock

Classical Mechanics Level 5

A clock is made out of a disk of radius \(R = 10~\mbox{cm}\) which is hung by a point on its edge and oscillates. All of a sudden, a circular part right next to the hanging point of radius \(\frac{R}{2}\) falls off, but the clock continues oscillating. What is the absolute value of the difference in s between the periods of oscillation before and after the part fell off?

Details and assumptions

  • Gravitational acceleration is \(g = 9.81~\mbox{m/s}^2\)
  • Amplitude of the vertical oscillations is small
  • The axis of rotation of the disc is horizontal all the time
  • The disc is homogeneous

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