lingesh said:Hi,
I am a bit confused about the units of MI...I read that MI of rectangle is b*d^3/12,so unit is mm^4..Also i read in wiki that unit of MI is kg.mm^2...
Both are correct,but why this difference is?
Thanks...SteamKing said:You are getting two different moments of inertia confused.
The area moment of inertia, sometimes called the second moment of area, has units of L4. The second moment of area of a rectangle is bd3/12, when referenced to the centroid of the rectangle. The area moment of inertia is chiefly used to determine things like bending stresses in beams.
https://en.wikipedia.org/wiki/Second_moment_of_area
The mass moment of inertia, sometimes abbreviated MOI or MMOI, is a slightly different concept. The MMOI has units of M L2.
The MMOI relates the torque applied to a body to its angular acceleration, T = I α, and is analogous to F = ma for rectilinear motion.
https://en.wikipedia.org/wiki/Moment_of_inertia
The moment of inertia, also known as angular mass or rotational inertia, is a measure of an object's resistance to changes in its rotational motion. It is a property of an object that depends on its mass distribution and the axis of rotation.
The moment of inertia is calculated by taking the integral of the mass of each individual particle in the object multiplied by the square of its distance from the axis of rotation.
The units of moment of inertia depend on the units used for mass and distance. In the SI system, the units are kilograms times meters squared (kg·m²). In the CGS system, the units are grams times centimeters squared (g·cm²).
Moment of inertia is important because it is a critical factor in determining an object's rotational motion. It explains how different objects will respond to forces applied to them and helps us understand and predict the behavior of rotating systems.
The moment of inertia affects an object's rotational motion by determining its angular acceleration in response to an applied torque. Objects with larger moments of inertia will have a slower angular acceleration, while objects with smaller moments of inertia will have a faster angular acceleration for the same amount of torque applied.