Two masses (M1 and M2) are connected by a thin massless rod of length L.(adsbygoogle = window.adsbygoogle || []).push({});

a) Determine the location of an axis perpendicular to the rod) which minimizes the moment of inertia of the system.

The answer is "with M1 at the origin x = M2*L/(M1+M2)

I know that I = Sum of ( M1*r1^2)

However, how do we know that M1 is at origin? I know that M1 + M2 is the total mass of the system. I know L is the length between the two points. But I don't know why the answer is above. I think I am missing something in understanding this but I don't know what.

b) Verify that the moment of inertia about this axis can be obtained by determine I about an axis through M2 and then using the parallel-axis theorem.

I know that I = I_cm + Mh^2 , where h is the distance between the axis, M is the total mass (M1+M2). Is the distance between the axis L? How do I use this to verify the moment of inertia.

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Find axis to minimize moment of inertia

**Physics Forums | Science Articles, Homework Help, Discussion**