It's allot simpler in two dimensions
[ I11 I12 ]
[ I12 I22 ]
moment of inertia is just the mass times the square of perpendicular distance to the rotation axis, i.e. I = mr2. That point mass relationship becomes the basis for all other moments of inertia since any object can be built up from a collection of point masses.
so if we put the center of mass to one side of our circle or Sphere. And that side gets a glacing blow it will make the circle or Sphere spin more rapidly that if it was hit further way from the center of mass.
Am I right in saying all it is, is a fence three dimensional lever. Move the short end of the lever and the long end moves the distance the short end moved divided by the length of the short end X the length of the long end. So if the short end was 10 cm long (distance from the pivot) and the long end was 30 cm long (distance from the pivot) if the short end was move 5 cm then the long end would move 3X that (15cm) 5cm / 10cm * 30cm = 15cm
It that right or have I got the wrong end of the lever :)
[ I11 I12 ]
[ I12 I22 ]
moment of inertia is just the mass times the square of perpendicular distance to the rotation axis, i.e. I = mr2. That point mass relationship becomes the basis for all other moments of inertia since any object can be built up from a collection of point masses.
so if we put the center of mass to one side of our circle or Sphere. And that side gets a glacing blow it will make the circle or Sphere spin more rapidly that if it was hit further way from the center of mass.
Am I right in saying all it is, is a fence three dimensional lever. Move the short end of the lever and the long end moves the distance the short end moved divided by the length of the short end X the length of the long end. So if the short end was 10 cm long (distance from the pivot) and the long end was 30 cm long (distance from the pivot) if the short end was move 5 cm then the long end would move 3X that (15cm) 5cm / 10cm * 30cm = 15cm
It that right or have I got the wrong end of the lever :)