moment of inertia

[mr_joshua]

There are 2 questions that are giving a few of us problems.

1. Find the moment of inertia of a rod about an axis through its center if the mass per unit length is A=A*x A is linear density. This is a simple problem, but we are not sure how to use the given value for A (linear density). so far we have I=A * intergral of x^2 dx from 0 to L/2. which you finally get 1/12ML^2...



2. Same type of inertia problem except this is a disk about its center where mass density Q (which in normal cases is dm/dA) here Q=Q*r^(-1)

Please help.

[e(ho0n3]

The statements
- A = A*x
- Q = Q*r^(-1)
don't make any sense.

Remember the definition of moment of inertia:

\int_V \rho(\mathbf{r})dV(r\sin\theta)^2

where θ is the angle between r and the axis of rotation and ρ(r) dV is the mass element at location r. If ρ(r) isn't constant you can't take it out of the integral.