hope you are all doing well.
I am taking a course at Coursera about Robotics and in one of the quizes, I had some problem with a particular question. I passed the quiz (4/5 correct answers), however I would like to know what was wrong with my approach. The discussion forums of the course are pretty useless. I had tried them for some questions in the past and I did not get even a single response from anybody. This is the reason I am posting the question here. Here is the question:
What I did was; I first divided the dumbbell into three parts: two spheres and one cylinder. Then I calculated the mass of the cyliner (1.4074) and then the mass of one of the spheres (23.52). Then I calculated the moment of inertia for each axis of the cylinder (Ix = 0.000281, Iy = 0.0048, Iz = 0.0048). After that, I did the same thing for one of the spheres (Ix = 0.0941, Iy = 0.0941, Iz = 0.0941) and multiplied each axis by 2. Then I added this result to first cylinder and I got the matrix;
[0.1885 0 0; 0 0.1930 0; 0 0 0.1930]. However, my result was incorrect. Can you tell me what was wrong with my approach?