How Do You Calculate the Moment of Inertia for a Compound Physical Pendulum?

[AdanSpirus]

1. Homework Statement
Ok So here's my question.
The physical Pendulum consists of a thin rod of mass m = 100 g and length 80 cm, and a spherical bob of mass M = 500 g and radius R = 25 cm. There a pivot P at the top of the rod.
(Sorry, I don't have a picture >.<)
a) It asks for the center of mass(I already got it)

b) It asks for the moment of Inertia

c)Calculate Net Torque

d) Find Angular Freq. of small oscillations

e) At t= 0, the pendulum position is theta = (theta)max / 2, where (theta)max is the amplitude , and theta is increasing. When is the next instance where the particle will have a speed that is one third of its maximum?

2. Homework Equations
I = Icm + Md^2
Sphere = 2/5MR^2
Rod = 1/2MR^2

Center of Mass = (m*l + M(R+l)/(m+M)

s = Acos(wt + phi)
v = -wAsin(wt + phi)
a = -w^2Asin(wt+ phi)

3. The Attempt at a Solution

I have got the center of mass which results to be 0.605 m.
The only problem I have is that I am not sure about the moment of Inertia considering there are 2 objects and I am not exactly sure of how to set up the moment of inertia equation with the Sphere and the Rod. This is what is only bugging me atm, I probably can do the rest if I figure out the moment of inertia >.< But I might post back after if I don't get the rest of the question.

 

[betel]

The formula for your center of mass is not quite correct for the rod part. I don't know how you calculated 0.6 form that.
This result is obviously wrong. 0.6 is still in the rod. But the rod in total has only 100g whereas the sphere has 500g. So the center of mass should be somewhere >0.8.

The whole point of the first part was to replace the two objects (which are themselves extended objects) by one object. The center of mass. No for this object the formulat for the moment of inertia holds.