Hey all,
Perhaps this is a bit stupid...
I'm familiar with the normal procedure of calculating rotational inertia (using integration, parallel axis theorem, etc.). However, I had a confusing thought: if the center of mass of a body is the point at which you can treat as all of the mass being concentrated there and also all the external forces, then why can't I say something like this:
If a uniform rod of length L is swinging around a pivot, and the center of mass of the rod is a distance L/2 away from the pivot, then why can't we treat that center of mass as the place where all the mass is concentrated and use the rotational inertia formula for a particle (MR^2) and subsequently get M(L/2)^2? I know it's ML^2/3, but what is the problem here?
Perhaps this is a bit stupid...
I'm familiar with the normal procedure of calculating rotational inertia (using integration, parallel axis theorem, etc.). However, I had a confusing thought: if the center of mass of a body is the point at which you can treat as all of the mass being concentrated there and also all the external forces, then why can't I say something like this:
If a uniform rod of length L is swinging around a pivot, and the center of mass of the rod is a distance L/2 away from the pivot, then why can't we treat that center of mass as the place where all the mass is concentrated and use the rotational inertia formula for a particle (MR^2) and subsequently get M(L/2)^2? I know it's ML^2/3, but what is the problem here?