Calculating Moment of Inertia. For a discrete collection of point masses we found ∑m;r For a continuous solid object we have to add up the mr2 contribution for every infinitesimal mass element dm dm Ne have to do an integral to find l rdm Physics 121: Lecture 18, Pg 11
Physics 121: Lecture 18, Pg 11 Calculating Moment of Inertia... For a discrete collection of point masses we found: For a continuous solid object we have to add up the mr2 contribution for every infinitesimal mass element dm. We have to do an integral to find I : I = = m r i i i N 2 1 r dm I = r dm 2
Moments of Inertia Some examples of i for solid objects I-MR Thin hoop(or cylinder)of mass M and radius R, about an axis through its center R perpendicular to the plane of the hoop I=-MR Thin hoop of mass m and radius r about an axis through a diameter Physics 121: Lecture 18, Pg 12
Physics 121: Lecture 18, Pg 12 Moments of Inertia Some examples of I for solid objects: Thin hoop (or cylinder) of mass M and radius R, about an axis through its center, perpendicular to the plane of the hoop. I = MR2 R I = 1 2 2 MR Thin hoop of mass M and radius R, about an axis through a diameter. R