# Moment of inertia of an object with uneven distribution of weight

1. Aug 10, 2011

### sungj25

I'm doing an experiment and I have to calculate calculate rotational kinetic energy of this can rolling down an inclined plane.
According to the equation, Er=1/2Iw^2, I=mr^2, and w=v/r (no slipping effect) right?
but doesn't I=mr^2 apply only when the weight is evenly distributed throughout the axis?

In my experiment, I'm going to add mass only on one side of an empty cylindrical can (using bluetag). Will I be still able to calculate the inertia using this I=mr^2 equation?

2. Aug 10, 2011

### Pi-Bond

The general formula for calculating the moment of inertia of a body about an axis is:

$I=\int r^{2} dm$

where r represents the distance of the mass element from the rotational axis. If the distance from the axis is so large that the distribution of the mass becomes negligible, then the formula you mention (mr2) is applicable. (for example the moment of inertia of the earth about the sun).

For your experiment you will need to use the general formula to account for the manner in which you distribute your bluetag. You might want to distribute the bluetag in a manner to simplify the integral.