Question

Position of centre of mass of annular disc is :-

Answer 1

Answer:

An annular disc has a mass m, inner radius R and outer radius 2R. The disc rolls on a flat surface without slipping. If the velocity of the centre of mass is v, the kinetic energy of the disc

Answer 2

Assuming that the density of the region is uniform, the yy coordinate of the center of mass is given as

yc=∫Rydxdy∫Rdxdyyc=∫Rydxdy∫Rdxdy

The region, RR, you are interested in i.e. the semi-annular plane as shown below.Converting this to polar coordinates, note that the rr varies from 11 to 22while θθ varies from 00 to ππ. Now you should be able to the integral.