Question

what is moment of inertia .

Answer 1

The moment of inertia, I, is defined as the ratio of an applied torque to the angular acceleration along a principal axis of the object,
\[I = \frac{ \tau }{ \alpha }\]Each of three mutually perpendicular axes in a body about which the moment of inertia is at a maximum are the principal axes.

Answer 2

It is a measure of 'resistance to turning'

Imagine a flat circular plate with a central axis. If you try to spin this plat you need to apply a turning force (torque)
If you took a plate of the same diameter and mass - but all the mass was around the perimeter (like a flywheel or bicycle rim) then you will need more torque to achieve the same angular acceleration.

It is calculated by the sum of the mass of each point times the square of the distance from the axis (this normally requires integral calculus to work out - but for some regular shapes it can be done from the geometry)

Answer 3

http://hyperphysics.phy-astr.gsu.edu/hbase/mi.html

Answer 4

@walpurgishacked
I think the MOI is MINIMUM about principal axis - not maximum

Answer 5

@MrNood "A principal axis may be simply defined as one about which no net torque is needed to maintain rotation at a constant angular velocity." - hyperphysics.

Also http://www.physics.arizona.edu/~varnes/Teaching/321Fall2004/Notes/Lecture34.pdf

Pretty sure it's a maximum.

Answer 6

@MrNood Also https://www.google.co.uk/#q=define+principal+axis

Answer 7

http://hyperphysics.phy-astr.gsu.edu/hbase/parax.html

The parallel axis theorem says that you ADD MOI as you deviate from the axis through CoG

I think your dictionary definition is incorrect

Answer 8

It is also intuitive - if you have a mass on the end of a very long light beam then the torque to rotate it is much higher then if you spin it about its axis .

Answer 9

So in linear, translational motion you have mass. For angular motion, you have moment of inertia. They are in a sense the same thing.

For instance, kinetic energy for linear motion is \[K=\frac{1}{2}mv^2\] where K is kinetic energy, m is mass and v is linear velocity. Another expression for kinetic energy is for objects rotating around a point with an angular velocity instead of linear velocity. \[K=\frac{1}{2}I \omega ^2\] here I is moment of inertia and omega (w) is the angular velocity.

This also holds true for other important relations, such as between linear momentum and angular momentum.

Answer 10

@MrNood Hmm, mechanics isn't really my field; I'm just trying to recall what I can from my first year undergrad, so I concede. I seem have it in my head that the principal axes are perpendicular, not parallel. Don't want to be giving wrong information and confuse others.

Answer 11

Yes principal axes ARE perpendicular

My point is that for any principal axis (which always runs through Cof G) then you must ADD MOI to rotate about any other axis, therefore the MOI must be minimum about CofG i.e. about principal axis

Answer 12

is just rotational analogue of mass

Answer 13

Well Moment of Inertia is analogus to interia of motion( to resist the state of motion or state of rest, this is confined to 2d motion) now in 3D motion a body wil resist rotation or resist coming to rest while rotating! This is basic idea hope u underatand!