Tuesday, January 5, 2016

Shift in Center of Mass When a Portion Removed Problem and Solution

We know that center of mass of shifts a new and heavy position of the system when a certain mass is removed. Basing on the concept, we would like to solve two problems. We would like to measure the shift in the center of mass of disc and sphere when a certain portion of the mass is removed from one side of the body. If the mass of the system is removed from the center of mass of the system, center of mass of the system remains the same.

For a two dimensional body like disc, mass is directly proportional to the area of the disc. It is simply because mass is the product of volume and density of the disc. Volume can be further can be written product of area of the disc and thickness of the disc. As thickness is same, mass of the disc is directly proportional to the area of the body. Area is further directly proportional to the square of the radius of the disc.

We can use the mathematical derivation that we have derived in the previous post to measure the shift in the center of mass of the system as shown in the video below.




Shift in the center of mass of sphere when a portion of the sphere is removed

In the same way, we can also  measure the shift in the center of mass of a sphere when a portion of mass is removed from it from one side. The only difference in this case when compared with the disc, is sphere is a three dimensional body. Hence mass of the body is directly proportional to the volume of the sphere. It means, mass of the sphere is directly proportional to the cube of the radius of the cube. The problem can be further solved as shown in the video below.






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