Theory of Machine
The rotating shafts tend to vibrate violently at whirling speeds because

The system is unbalanced
Bearing centre line coincides with the axis
The shafts are rotating at very high speeds
Resonance is caused due to the heavy mass of the rotor

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Theory of Machine
The frictional torque transmitted in a flat collar bearing, considering uniform pressure, is (where r₁ and r₂ = External and internal radii of collar respectively)

(2/3). μ W (r₁ + r₂)
(2/3). μ W [(r₁³ - r₂³)/(r₁² - r₂²)]
(1/2). μ W (r₁ + r₂)
(1/2). μ W [(r₁³ - r₂³)/(r₁² - r₂²)]

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