A uniform rectangular plank of mass M, length L, width 2d, and thickness 2a is balanced horizontally on a fixed cylinder of radius R, with its length parallel to the axis of the cylinder. Assuming that the plank rolls without slipping on the cylinder, find the condition for stable equilibrium of the plank and the frequency of small oscillations. The moment of inertia of the plank about an axis parallel to the cylinder axis and passing through its center of mass is 1 Iom Ian = M (d + a*).
A uniform rectangular plank of mass M, length L, width 2d, and thickness 2a is balanced horizontally on a fixed cylinder of radius R, with its length parallel to the axis of the cylinder. Assuming that the plank rolls without slipping on the cylinder, find the condition for stable equilibrium of the plank and the frequency of small oscillations. The moment of inertia of the plank about an axis parallel to the cylinder axis and passing through its center of mass is 1 Iom Ian = M (d + a*).
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Transcribed Image Text:A uniform rectangular plank of mass M, length L, width 2d, and thickness 2a is balanced
horizontally on a fixed cylinder of radius R, with its length parallel to the axis of the
cylinder. Assuming that the plank rolls without slipping on the cylinder, find the condition
for stable equilibrium of the plank and the frequency of small oscillations. The moment
of inertia of the plank about an axis parallel to the cylinder axis and passing through its
center of mass is
1
Iom
Ian = M (d + a*).
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