Halliday, Resnick & Walker — Oscillations: Problem Problem_109

Oscillating marmoset. In Fig. 15.44, a marmoset of mass \( m_2 \) clutches a massless cord wrapped around a disk, of radius \( R = 20 \text{ cm} \) and mass \( M = 8m_2 \), that pivots about a horizontal axis through the center of mass at \( O \). Mass \( m_1 (= 4m_2) \) is attached to the disk at a distance \( r = R/2 \) from \( O \). (a) When the disk + marmoset + \( m_1 \) system is in equilibrium, what is angle \( \phi \) between the vertical and a line from \( O \) to \( m_1 \)? (b) In terms of \( m_2 \) and \( R \), what is the rotational inertia \( I \) of the system about \( O \)? (c) The disk is rotated counterclockwise from equilibrium through a small angle \( \theta \) and released. What is the angular frequency \( \omega \) of the resulting simple harmonic motion?