The discussion revolves around calculating the center of mass (C.M.) of a semicircular disk using the known C.M. of a semicircular arc. Participants explore the relationship between these two shapes and the methods for deriving one from the other.
There is an ongoing exploration of methods, with some participants providing insights into how to approach the problem. Questions remain about the technical aspects of these methods and how to apply them effectively.
Participants express confusion regarding the differences between the arcs and the implications for calculating the C.M. Additionally, there is a discussion about the relevance of centroids of triangles in relation to the semicircular arc.
sr-candy said:just consider the disk is formed with many semi circular arcs
and for the converse case ,
there are 2 methods
1. consider the CM a semi circular shell, ie. a (disk) - (another disk with smaller radius), then take limit for the radius of the small one approach the bigger one
2. consider the semi circular disk as many triangular laminar...
jessicaw said:"just consider the disk is formed with many semi circular arcs" but isn't the arcs different from each other? I thought of this at first but get stuck. How to do this techinically?
"2. consider the semi circular disk as many triangular laminar..."Triangle??confused.Why?and what do you mean by traingular "laminar"?
sr-candy said:2. laminar means layer or plane etc. Just think that a semi circle is formed with many sectors, when the sectors become smaller, it will look like many triangle.
jessicaw said:i understand this now, but how can i use this fact to calculate the C.M of arc? The C.M of triangle is the centroid but the centroid is not on the semicircular arc. So how to use this fact?