Find the Center of Mass of a Circular Region with a Missing Segment using Double Integration

Опубликовано: 31 Октябрь 2024
на канале: John's Maths Book

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This video evaluates the double integrals, utilizing polar coordinates, found in the video.
• Find the Region of a Circle with a Missing...

It then proceeds to use the results to find the center of mass of a circle with a missing segment.

The inner integrals are evaluated first along r summing all the infinitesimally small slices dr, followed by the evaluation of the outer integral from 0 to alpha and then from alpha to pi/2. This sums all the infinitesimally small slices of d(theta). The results of the double integrals are then summed. This gives the weighted average of x over the uniform region. Dividing this by the area of the region gives the center of mass of the region.

The calculations re check by setting appropriate values for a and b.