A pivot bearing used on the shaft o an electrical instrument...

A pivot bearing used on the shaft o an electrical instrument is shown in Fig. $P 1.86 .$ An oil with a viscosity of $\mu=0.010 \mathrm{lb} \cdot \mathrm{s} / \mathrm{ft}^{2}$ fills the 0.001 -in. gap between the rotating shaft and the stationary base. Determine the frictional torque on the shaft when it rotates at 5000 rpm.

Key Concepts

Viscosity

Viscosity is a measure of a fluid's resistance to flow or deformation. It characterizes how strongly a fluid resists shearing forces, which is critical in lubrication applications where a thin fluid film separates moving surfaces.

Newton’s Law of Viscosity

Newton’s Law of Viscosity states that the shear stress between adjacent fluid layers is proportional to the rate of change of velocity with respect to distance (velocity gradient). This relationship is fundamental to calculating the frictional forces in viscous flows between surfaces.

Shear Stress in Fluids

Shear stress arises in a fluid when layers move relative to each other at different velocities. In the context of lubrication, this shear stress is responsible for generating friction that can be integrated over a surface to determine forces such as frictional torque.

Frictional Torque

Frictional torque in a system is generated by the viscous shear forces acting along the surface of a rotating object. It is determined by integrating the shear stress over the area of the surface, taking into account the geometry and relative motion between surfaces.

Angular Velocity Conversion

Converting rotational speed units (such as rpm to rad/s) is essential for calculations involving rotational systems. Accurate conversion ensures that the shear rate and resulting frictional effects are computed correctly in the analysis of rotating machinery.

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