00:01
So this question belongs to the moment of inertia in which we have to determine the moment of inertia of a solid cylinder of mass capital m, radius capital r, and length l, about an axis y y, which is passing through its center of mass and perpendicular to the axis.
00:17
So suppose this is the body diagram of the cylinder and this is our axis y y which is passing through the center of mass and this is the radius.
00:31
Of the cylinder, this is the vertical axis, and this will be the radius, and this is the length, this is length l.
00:41
So this length will be l by 2, and let us suppose an element at this distance, z, in this direction, and this width has dz.
00:55
So if the total cylinder has total mass capital m, then the mass of this element will be d, and which can be calculated as dm, this will be equals to density multiplied by volume and volume for this element will be pi r square multiplied by tz.
01:14
Pi r square will be the cross -sectional area multiplied by width, so this will be the volume, so this will be the mass of this element.
01:22
Now the moment of inertia for this element can be written as d .i, it is equals to d .m multiplied by r square by 4, about an axis y, y...