A rotor has a mass of 12 kg and is mounted midway on a horizontal shaft which is supported at the ends by two bearings (assumed as simply supported). The bearings are 1 m apart. What will be the critical (whirling) speed of the shaft? [EI = 4 kN - m2, g = 10 m/s2]

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  1. 40 rad/s
  2. 300 rad/s
  3. 400 rad/s
  4. 30 rad/s

Answer (Detailed Solution Below)

Option 1 : 40 rad/s
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Detailed Solution

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Concept:

For a simply supported shaft with a rotor (concentrated mass) at the center, the critical (whirling) speed is determined using the relation:

Where, is the static deflection due to the weight of the rotor.

Static deflection at center of simply supported shaft due to point load is given by:

Calculation:

Given:

Mass of rotor, 

Span of shaft, 

Substitute in deflection formula:

Now, critical speed:

 

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