00:01
Calculate the moment of inertia about an axis through the geometric center of the rod.
00:05
So we can say that we're going to select a differential element of the rod of length dx.
00:10
So this would be the differential length essentially.
00:13
And it would be at a distance x from the center of the rod here.
00:18
This dash line represents the essentially the axis of rotation.
00:23
Because the mass density changes uniformly from the initial.
00:31
Mass density we can say that here we can say that here x we have the initial mass density at rather we can say x equals rather negative l over 2 and then we can say that this will be three times the initial mass density at x equaling l over 2 so here we can say that the mass then mass density function lambda this would be equal to 2 times lambda multiplied by one over one, rather one plus x over l.
01:17
And we're essentially finding the mass of the differential element.
01:23
So we can say dm is equaling lambda dx.
01:27
This is going to be equal to two lambda one plus x over l multiplied by dx.
01:37
And so now we're going to use equation 1016...