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
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