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Now imagine a massive particle dropped in with zero angular momentum. The angular velocity is given by d /d p d = = t dt dt/d p With p = 0, we have p t = g tt pt and p = g t pt and so this expression becomes, using (11.17), g t 2mar p = tt = = t 2 + a 2 )2 a 2 sin2 p g (r Note that the angular velocity is proportional to terms that make up the metric, and so think of it as being due to the gravitational eld. Therefore, we see that if we drop a particle in from in nity with zero angular momentum, it will pick up an angular velocity from the gravitational eld. This effect is called frame dragging and it causes a gyroscopic precession effect known as the Lense-Thirring effect. In the equatorial plane we have = 0 and so sin2 = (1/2) (1 cos 2 ) = 0, giving a simpli ed expression for the angular velocity given by = 2mar (r 2 + a 2 )2

Capabilities of Visual Inspection Visual inspection serves a number of important purposes well, but it also has several important limitations. 53.6.4.1 Advantages. Visual inspection can be an accurate and cost-effective method of defect detection for nonsubjective defects, such as larger missing components, larger misoriented or reversed components, or solder bridges. When low volume or lack of technical resources prevents the use of automation or more sophisticated tools, visual inspection is one alternative that finds many of the more subjective defects, such as solder joints with insufficient solder, lifted leads, or poor wetting. Finally, visual inspection can quickly detect when a process step has drifted significantly out of its control limits. 53.6.4.2 Disadvantages. Visual inspection also has many limitations, including the following:

Low coverage of solder joint defect detection repeatability, particularly for fine-pitch parts, which results in high false accepts or defect escapes and high false reject rates Low coverage of component defect detection repeatability for smaller components such as 0402, 0201, or 01005 passive components Inability to see hidden solder joints in component types such as some connectors, PGAs, BGAs, chip-scale packages (CSPs), SIPs, or multichip modules (MCM) Inability to collect quantitative measurements in addition to defect data

53643 Repeatability Limitations Several studies have documented the low repeatability rate of visual inspection of solder joints One such study was conducted by AT&T at its Federal Systems Division1 This study showed that even the same inspector inspecting the same assembly twice had a defect call repeatability rate of only about 50 percent Two different inspectors inspecting the same assembly had a defect call repeatability rate of only about 28 percent This study did not include any very-fine-pitch SMT solder joints or 0603 passive components, which are more difficult to inspect visually To alleviate this severe limitation somewhat, manufacturers have implemented the use of microscopes with a magnification level of 10 Often, stereoscopic microscopes are used to provide visual inspectors a better three-dimensional view Not as frequently, manufacturers have implemented light sources and cameras to capture real-time magnified video images of the assembly being inspected.

The lighting and high-resolution video images can make it easier for visual inspectors to see the acceptance criteria for which they are searching These enhancements do improve the repeatability rate of visual inspection But the requirement for subjective human calls and the tedium of carefully inspecting thousands of connections per hour still results in repeatability rates much lower than desired Low repeatability means many missed defects that escape to final assembly or to customers, impacting reliability and wasting and possibly damaging rework of good connections 53644 Hidden Solder Joints Several component types used in printed circuit assemblies do not provide visual access to solder joints These components include packages with bump arrays where the solder joints are distributed in a matrix under the entire component body, such as ball grid arrays and chip-scale packages.

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For these components, all of the joints except those on the edges of the array are completely hidden from view Other packages, such as J-leaded components, where the connections are under the component body at the component edges, and 05 mm-pitch gull-wing components, where the solder joint heel is only 008 mm high and behind the component leads, also make visual inspection more difficult Some manufacturers have attempted to solve this problem by using a penetrating imaging technique, such as x-ray, acoustics, or thermography, to acquire a live, magnified video image that the visual inspector can look at to make a defect call However, the images resulting from.