center of mass and moment of inertia of four masses system

Please see problem attached.

The four masses shown in Figure Ex13.17 are connected by massless, rigid rods, with m = 184 g.
(a) Find the coordinates of the center of mass.
(b) Find the moment of inertia about a diagonal axis that passes through masses B and D.

The solution is comprised of detailed explanations of finding the center of mass and moment of inertia of four masses connected by massless rigid rod system.

Ball a, of mass m_a, is connected to ball b, of mass m_b, by a massless rod of length L. The two vertical dashed lines in the figure, one through each ball, represent two different axes of rotation, axes a and b. These axes are parallel to each other and perpendicular to the rod. The moment of inertia of the two-masssystem abou

Prim is primitive!
In genral the moment of inertia around an axis( a line) L is:
Isubl=double prim (dist(.,L)^2*delta*dA)
The collection of lines parallel to the y axis have the form x=a .Let I=Isub(y) be the usual moment of inertia around the y axis
I= double prim of x^2*delta*dA
Let I(bar) be the moment of ine

A thin, uniform rod has length L andmass M.
a. Find by integration its moment of inertia about an axis perpendicular to the rod at one end.
b. Find by integration its moment of inertia about an axis perpencicular to the rod at its center of mass.

A uniform cylinder, mass M= 12 kg, radius R= .36 m, is initially rotating about a vertical axis through its center at angular velocity wo= 6.6 rad/sec. Now two small (point masses), each of mass m= 2 kg, are dropped onto and stick to the cylinder, each at distance r= .24 m from the axis. SEE ATTACHMENT for diagram.
Find wf, t

The L-shaped object in Figure 11-27 consists of three masses connected by light rods. See attached Figure.
(a) What torque must be applied to this object to give it an angular acceleration of 1.27 rad/s2 if it is rotated about the x axis?
_________N?m
(b) What torque must be applied to this object to give it an angular acc

(See attached file for full problem description with equations)
(Steiner's theorem) If IA is the moment of inertia of a mass distribution of total mass M with respect to an axis A through the center of gravity, show that its moment of inertia IB with respect to an axis B, which is parallel to A and has the distance k from it,

To solve many problems about rotational motion, it is important to know the moment of inertia of each object involved. Calculating the moments of inertia of various objects, even highly symmetrical ones, may be a lengthy and tedious process. While it is important to be able to calculate moments of inertia from the definition, in

A sphere consists of a solid wooden ball of uniform density 800kg/m^3 and radius 0.20 m and is covered with a thin coating of lead foil with area density 20kg/m^2 .
Calculate the moment of inertia of this sphere about an axis passing through its center.