Oscillation of disk and particle.

1. The problem statement, all variables and given/known data

A disk of mass M(=2 kg)and radius R(=5m) is pivoted at the center. The disk lies in the vertical plane and is free to rotate about the pivot .A particle of mass (=1 kg) is on the periphery of the disk. Find the time period of small oscillation of the system .

2. Relevant equations

3. The attempt at a solution

If the disk is fixed then the time period of oscillation is simply 2π√(R/g). But here the disk is free to rotate so that adds to the complexity.

Let the particle be at an angular displacement θ towards right side .If the particle slides down, the disk should move towards right so that horizontal coordinate of CM doesn’t change.But then we have the pivot force so that condition doesn’t hold.

Both the particle and the disk are moving which make things quite difficult .

I have made a sketch depicting the forces on the disk and the particle.

I would be grateful if someone could help me with the problem.

Attached Images
File Type: gif disk.GIF (2.6 KB)
File Type: gif particle.GIF (3.3 KB)
File Type: gif disk_fbd.GIF (3.4 KB)


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