The base B has a mass of 6.3 kg and a radius of gyration of 126 mm about the cen

Question

The base B has a mass of 6.3 kg and a radius of gyration of 126 mm about the central vertical axis shown. Each plate P has a mass of 3.2 kg. If the system is freely rotating about the vertical axis with an angular speed N1 = 17 rev/min with the plates in the vertical position, estimate the angular speed N2 when the plates have moved to the horizontal positions indicated. Neglect friction.

The base B has a mass of 6.3 kg and a radius of gyration of 126 mm about the central vertical axis shown. Each plate P has a mass of 3.2 kg. If the system is freely rotating about the vertical axis with an angular speed N1 = 17 rev/min with the plates in the vertical position, estimate the angular speed N2 when the plates have moved to the horizontal positions indicated. Neglect friction.

Explanation / Answer

For plates in vertical postion ..

inertia of 1 plate (Ip1 ) = (1/12)*3.2* 0.31^2 + 3.2*0.185^2 = 0.13514 kg m^2

so intial inertia of system I1 = 6.3*0.126^2 + 2*Ip1 = 0.37029 kg m^2


For plates in horizontal postion ..

inertia of 1 plate (Ip2 ) = (1/12)*3.2* (0.310^2 + 0.51^2) + 3.2*((0.51/2) +0.185)^2 = 0.7145 kg m^2

so final inertia of system I2 = 6.3*0.126^2 + 2*Ip1 = 1.5290 kg m^2



so.. conserving momentum
I1 * N1 = I2 * N2
so.. 0.37029 * 17 = 1.5290 * N2

so.. N2 = 4.117 rev/min

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