# Homework Help: Calculating new moment of inertia matrix with a new center of mass

1. Nov 7, 2012

### tlonster

1. The problem statement, all variables and given/known data
The total length of the composite body is 4.5 feet. Before the propellant is burned, the projectile weighs 23 lbf. After the propellant burns, the remaining projectile weighs 16 lbf. Before the propellant is burned, the mass center is located 2.6 feet from the projectile base along the axis of symmetry and the mass moment of inertia components are: Ixx=0.005 slug ft^2, Iyy = 2.1 slug ft^2, Izz=2.1 slug ft^2, Ixy = Ixz = Iyz = 0 slug ft^2. Compute the mass center location and mass moment of inertia matrix after the propellant has burned.

2. Relevant equations
I have already calculated the new center of mass as 3.41 (where CM is for the rocket body) How do I find the new moment of inertia matrix?

3. The attempt at a solution

Do I just take the difference between the two CM's, multiply that value with each component given in my moment of inertia matrix, and then add that result to the initial given matrix?

Your help is appreciated!

2. Nov 7, 2012

### SteamKing

Staff Emeritus
Without knowing the c.g. of the propellant (or how its mass was distributed within the rocket body), how did you calculate the c.g. of the rocket after the propellant had burned?
Similar questions would be raised about the moment of inertia calculation. Without knowing the MOI of the rocket fuel about its c.g., the MOI of the rocket after fuel is burned cannot be calculated.

3. Nov 7, 2012

### tlonster

woops, I left that out of the problem statement. from the base of the rocket, the cylinder that has the propellant is 1.5 ft. long. I just used then 7lbf for the propellant at CM of .75 ft to get the CM accociated with just the structure.

Basically set up this....

[7(.75) + 16x]/23 = 2.6 where x returns the location of my CM for the structure only

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