It is the measure of how difficult something is to rotate. For example take a steal rod. If you hold it in the middle, it rotates easily. If you hold it at one end it is much harder to rotate (try it!). If you calculate the moment of inertia for a rod rotating about the middle it is 1/12 ML^2, if you do calculation for one end you get 1/3 ML^2. So you can see that the calculation for moment of inertia is a smaller number for the middle than for one end, which agrees with experimt
@jamdann21 ok were I is moment of inertia I=(M)L^2 were L is mass and L is the Length of the (radius) square.. Is there any formula to calculate Moment of Inertia all the time like whats the difference in the Integral I seen this one in a book { I= Integral r^2*dm} i dont get that! i know how to do integrals.. Do you i just you the chart with all the geometric shapes?
so I = integral of r^2 dm, as you say and this is its definition.
The chart you speak of, is just the solved above integral for specific situations.
For the simplest, a point mass or a hoop, r is a constant and comes out of integral, thus you get the trivial integral of dm, which is just m, thus you get I = mr^2.
For different geometries you need to put dm in terms of the density and dr. For a disc you integrate rings (where dm = density*2*pi*r*dr) from 0 to R and get I=.5mr^2
u made life easier......thanx!!!!
MyNaanu 1 month ago
Can you explain more on the torque part?
smellingthursdays 3 months ago
now that's what i call a good explanation, finally it's clear for me what is Moment of Inertia :) thank you sir
mariakas13 4 months ago
action :)
varmman 5 months ago
what is moment of inertia?
hypeblast 1 year ago
@hypeblast
It is the measure of how difficult something is to rotate. For example take a steal rod. If you hold it in the middle, it rotates easily. If you hold it at one end it is much harder to rotate (try it!). If you calculate the moment of inertia for a rod rotating about the middle it is 1/12 ML^2, if you do calculation for one end you get 1/3 ML^2. So you can see that the calculation for moment of inertia is a smaller number for the middle than for one end, which agrees with experimt
jamdann21 1 year ago
@jamdann21 ok were I is moment of inertia I=(M)L^2 were L is mass and L is the Length of the (radius) square.. Is there any formula to calculate Moment of Inertia all the time like whats the difference in the Integral I seen this one in a book { I= Integral r^2*dm} i dont get that! i know how to do integrals.. Do you i just you the chart with all the geometric shapes?
hypeblast 1 year ago
@hypeblast
so I = integral of r^2 dm, as you say and this is its definition.
The chart you speak of, is just the solved above integral for specific situations.
For the simplest, a point mass or a hoop, r is a constant and comes out of integral, thus you get the trivial integral of dm, which is just m, thus you get I = mr^2.
For different geometries you need to put dm in terms of the density and dr. For a disc you integrate rings (where dm = density*2*pi*r*dr) from 0 to R and get I=.5mr^2
jamdann21 1 year ago