Question

The static deflection of the shaft under the flywheel is 25 mm. Assuming g = 10m/s², the critical speed in rad/s will be:  

1. 30
2. 10
3. 40
4. 20

Answer 1

Correct Answer - Option 4 : 20

Concept

Critical speed

Whirling speed or Critical speed of a shaft is defined as the speed at which a rotating shaft will tend to vibrate violently in the transverse direction if the shaft rotates in horizontal direction. In other words, the whirling or critical speed is the speed at which resonance occurs.

Critical speed of the shaft:

\(\omega = \sqrt {\frac{g}{{\rm{Δ}}}} \)

Calculation:

Given:

Δ =  25 mm

\(\omega = \sqrt {\frac{g}{{\rm{Δ}}}} = \sqrt {\frac{{10}}{{25 \times {{10}^{ - 3}}}}} = \sqrt {\frac{{10000}}{25}} =\sqrt {400} =20 \)  rad/sec