center of mass of semicirculardisk calculated from center of mass of semicircular arc

jessicaw

i have calculated the C.M. of semi-circular arc of radius r and mass m.
How can i use this answer to calculate the C.M of semi-circular disk of radius r and mass m?
thanks:)

ps. how about the converse?

sr-candy

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

"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

1. yes the arcs are of different radius, but you have the CM of the arcs, so you can consider the mass of the arcs are all lying on the y axis, all you have to do is calculate the CM of these "CMs"

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

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?

sr-candy

Why not? the centroids of these triangles will form an arc