The base B has a mass of 5.8 kg and a radius of gyration of 85 mm about the cent

Question

The base B has a mass of 5.8 kg and a radius of gyration of 85 mm about the central vertical axis shown. Each plate P has a mass of 2.7 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 5.8 kg and a radius of gyration of 85 mm about the central vertical axis shown. Each plate P has a mass of 2.7 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)*2.7* 0.23^2 + 2.7*0.145^2 = 0.06867 kg m^2

so intial inertia of system I1 = 5.8*0.085^2 + 2*Ip1 = 0.179245 kg m^2


For plates in horizontal postion ..

inertia of 1 plate (Ip2 ) = (1/12)*2.7* (0.325^2 + 0.23^2) + 2.7*((0.325/2) +0.145)^2 = 0.29097 kg m^2

so final inertia of system I2 = 5.8*0.085^2 + 2*Ip1 = 0.623845 kg m^2



so.. conserving momentum
I1 * N1 = I2 * N2
so.. 0.179245 * 17 = 0.623845 * N2

so.. N2 = 4.88449 rev/min

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