The angular momentum of the system is conserved, so the final angular momentum of the system is equal to the initial angular momentum.
Initial angular momentum = 8kgm2 * 6 rev/s = 48 kgm2/s
Final angular momentum = (8kgm2 + 1.4kg * 1.2m2) * ωf
where ωf is the final angular velocity of the table.
Solving for ωf, we get:
ωf = 48 kgm2/s / (8kgm2 + 1.4kg * 1.2m2)
ωf = 4.5 rev/s
A rotating table has a moment of inertia about a vertical axis through its centroid of 8kgm2 and turns at 6 rev/s. A servo-piston of mass 1.4kg rotates with the table at initial radius of 1.2m. it then moves towards the center of rotation a distance of 600mm. Determine the final speed of free rotation of of the table
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