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Assuming the shaft to be freely supported. Calculate the whirling speed of the shaft : 2 cm diameter and 60 cm long carrying a mass of 1 kg at its mid-point. The density of the shaft material is 40 Mg/m3, and Young’s modulus is 200 GN/m2.

Assuming the shaft to be freely supported. Calculate the whirling speed of the shaft : 2 cm diameter and 60 cm long carrying a mass of 1 kg at its mid-point. The density of the shaft material is 40 Mg/m3, and Young’s modulus is 200 GN/m2. Correct Answer 2598

I = πd4/64 = 7.855×10-9 m4 d due to 1 kg mass = 28×10-6 m d due to mass of the shaft = 0.133×10-3m substituting these values into the frequency relation of transverse vibrations we get f = 43.3 Hz Therefore Nc = 43.3×60 = 2598 rpm.

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