1. The problem statement, all variables and given/known data I need to find the final impact speed of the flame of a non-uniform candle. I am given that the mass per unit length increases linearly from top to bottom starting with 1kg/m at the bottom and 10kg/m at the top. I need to find how fast the candle flame is moving once the candle hits the table. I also know the length of the candle, 2m 2. Relevant equations Xcm=1/M∫xdm m=Lλ dm=dxλ I=∫x2dm 3. The attempt at a solution If dm=dLλ then I have to find lamba ( which I'm unsure of how to do) then integrate from 0 to L to find the total mass. Then from there I can find the center of mass then rotational inertia and use energy to find the final velocity. Can someone tell me if I am thinking correctly and also help me find the total mass? Thanks in advance.