Hey, need a quick bit of help, Maths Physics end of year exam and I can't find how to calculate the moment of inertia of a non uniform bod thin rod.
I'll post the question here for reference -
1. A rod AB of length 3m has non-uniform density x 15 − 2xkg/m where x measures
distance (in m) from the end A of the rod.
a. Find the moment of inertia of the rod about an axis perpendicular to the rod through the end
b. Use your result to find the kinetic energy of the rod when it is rotating about the given axis
with angular velocity 2rad / s.
c. Deduce the moment of inertia of the rod about an axis parallel to the given axis but passing
through the centre of mass of the rod.
[Use the result in question 1 above for the location of the centre of mass.]
but I really just need the formula,
I = Sigma m.r^2 ?
The Attempt at a Solution
Around 3 A4 pages of pointlessness