Recent content by ravanbak

I find it hard to believe that knowing everything else (mass, length and center of mass) about the rod, the density at a given location cannot be calculated. Remember that I said the density changes linearly from one end to the other, it's not just random. Given the mass and center of mass, I...

Sorry, but can you clarify: are you saying there is no way to solve for actual values of linear density? My understanding is that even if I determine the ratio between ρ0 and ρL, I still won't be able to get density values without already knowing the density at some location.

Thanks, I'm trying. :) But it looks like I didn't explain it properly. I already know where the center of mass is located. I'm trying to find a way to solve for the linear density at a given location along the rod. Particularly, what is the linear density at x0 and at xL. Thanks, Dave

Hi Chet, Thanks very much for your help. It's been a long time since I've done any calculus, but here's what I have so far: Step 1: m = (ρL - ρ0) / L b = ρ0 So, ρ = (ρL - ρ0) / L * x + ρ0 Step 2: After integration, mass = (ρL + ρ0)L / 2 (which is the result I was expecting) Step 3: Ok...

I hope someone can point me in the right direction on how to solve this, and hopefully I can explain it properly. Given a rod with a known length, mass and center of mass, how can I find the linear density at a given location (x) along the length of the rod. I want to say 'instantaneous'...

Thanks very much for your help, tiny-tim! I'm going to think more about this and possibly ask more questions later.

Sorry, I'm aware that I don't know enough to even properly ask the question. I'm going to do some reading about tensors now. One more question: you said that the moment about an axis is derived from the inertia tensor. However, I don't have a tensor to begin with, only the 3 moments of...

Thanks for the reply. Yes, I do know it's not a vector and that there are 3 principal moments. My thought was to treat those 3 moments as a single 3D vector, or a 3D point in space, and then apply the same rotation as was applied to the object to that point to get a new moment. Just a...

Homework Statement I hope I can explain this properly: 1. Let's say you're given the mass moment of inertia of some non-uniform 3-dimensional object. 2. The moment is relative to coordinate system "CS1", with origin at the object's center of mass and about axes x, y and z. 3. Say...