- #1
slasakai
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Homework Statement
a rod of mass M and length L is supported by a smooth horizontal floor and leans against a smooth vertical wall, the mass density increases linearly with p=kr where r is the distance from the wall and k is a positive constant.
a.finf the moment of inertia of the rod with respect to the centre of mass.
b.the beam is released from a position of rest, at 60 degrees to the downward vertical, find the energy conservation equation of the beam.
Homework Equations
I=∫r^2 dm
The Attempt at a Solution
for part a, I considered a small length of rod, dl, and its mass as dm=(m/l)*dl
and using the fact that density ,p=m/l , m=krl
giving dm=kr dl , here's where I got stuck - I assumed that since dl and dr would be proportional you could simply replace dl with dr in this equation and integrate for mass and moment of inertia etc. doing it this way I got an answer for moment of inertia = (1/2)ML^2 which looks OK. But I am very uncertain about substituting dl for dr.
for part b I'm not completely sure how to even approach this, it would be wonderful if someone could verify my approach and perhaps give me a hint for part b.
thanks in advance,