Center of Mass of Standard Continuous Objects (Part-1)

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There are several continuous objects which are used frequently in problems based on different physical situations. Here we’ll study about localization of these standard objects

1. Center of Mass of a Uniform Half Ring: To locate the center of mass of a half Ring, we consider

a polar element on the circumference of Ring and find the center of mass by integrating it within

limits from -90 degree to +90 degree.

For detailed analysis, see the video below – https://youtu.be/bJWFgJTxIFk

2. Center of Mass of a Uniform Half Disc: To locate the center of mass of a half Disc, we consider

an elemental half ring at radius x and width dx on the surface of disc and find the center of mass

by integrating it within limits from 0 to R, the radius of disc.

For detailed analysis, see the video

below – https://youtu.be/xTJKSzHsHWw

3. Center of Mass of a Uniform Hollow Hemisphere: To locate the center of mass of a hollow

hemisphere, we consider an elemental ring of polar width d(theta) at an angle(theta) from the axis of

hollow hemisphere and find the center of mass by integrating it within limits from 0 to 90

degree.

For detailed analysis, see the video below- https://youtu.be/UiAH-Ev6PRA

4. Center of Mass of a Uniform Solid Hemisphere: To locate the center of mass of a solid

hemisphere, we consider an elemental disc at a distance x from center of hemisphere, the width

of elemental disc is taken as dx and find the center of mass by integrating it within limits from 0

to R, the radius of hemisphere.

For detailed analysis, see the video below – https://youtu.be/KBGsorVYqfo

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