Working out moment of interia?

[jewii]

it's says it's the sum of MR^2 but some objects are half, 2 times ETC, how do you decide the multiple of MR^2, like a sphere is actually just MR^2 but other objects are not.

 

[Mat]

(MR2/2)



Problem?

 

[Dunks]

Who cares, just remember these: http://en.wikipedia.org/wiki/List_of_moments_of_inertia

 

[p4radox]

Different objects have different moments of inertia because they're different shapes: simple as that. More mass at a greater distance from the axis means a bigger moment of inertia. Compare trying to spin a big, heavy flywheel with trying to spin a pencil about its own axis: massive difference. Either look them up from a table like this:

http://en.wikipedia.org/wiki/List_of_moments_of_inertia

and use the parallel and perpendicular axis theorems:
http://en.wikipedia.org/wiki/Parallel_axis_theorem
http://en.wikipedia.org/wiki/Perpendicular_axis_theorem

Or do it the hard way and integrate from first principles, see here:
http://en.wikipedia.org/wiki/Moment_of_inertia

 

[GreatAuk]

It's totally dependent on the shape of the object, it's mass (and distribution) and where you are rotating it about.

Common shapes will be in lists. For everything else, just add all the moments of inertia of every atom, that should give a fairly accurate answer.