The discussion revolves around a physics problem involving two rockets connected by a rod, focusing on concepts of rotational dynamics, center of mass, and moment of inertia.
Some participants have offered insights into the calculations and assumptions made, questioning the treatment of the rod and its moment of inertia. There is an ongoing exploration of different methods to approach the problem, with no explicit consensus reached yet.
Participants are discussing the implications of treating the center of mass as fixed versus moving, and there are references to specific formulas for moment of inertia that may not fully apply in the context of the problem.
haruspex said:Your answer would have been correct if the CoM had been fixed in space on an axle. What will happen instead?
haruspex said:Yes, thinking about this again I believe your method is correct, but in the calculation you treated the tunnel as a point mass at its centre. That slightly underestimates the moment of inertia of the system. I get 0.166. Is that error enough to explain your answer's rejection?
Use the parallel axis theorem. The MoI about one end is simply a special case of that.Esoremada said:That was correct! So what is the correct way to calculate the moment of a inertia of a rod about a given pivot? I only know that it is 1/12*ML^2 and 1/3*ML^2 for pivots about the centre or end.
Isn't it 12500?Esoremada said:Oh cool I never even noticed that. I get how to derive 1/3*ML^2 now but I try doing it in this problem and get it wrong
1250*(67.102 - 99/2)^2 + 1/12*1250*99^2
That's the moment of the rod rotating about its centre plus the moment of the rod's centre of mass rotating about the systems centre of mass. What am I doing wrong?