Engr Help

Moment of Inertia Click here for strategy to calculate moment of inertia

In a Nut Shell: Forces and/or moments acting on a rigid body in the x˗y plane produce

accelerated motion of the center of mass and angular acceleration about the center of mass

of the body. A moment acting on the body produces a response directly proportional to the

mass moment of inertia, I^C_z,K, taken about the mass center of the body, times the angular

acceleration of the body.

The basic equations for a body experiencing accelerated plane motion are:

F = m a_C

M = I^C_z,K α k

where F is the resultant external force acting on the body

m is the mass of the body

a_C is the acceleration of the center of mass of the body

M is the resultant moment of all external forces and couples acting on the body

I^C_z,K is the mass moment of inertia of the body about its mass center

α k is the angular acceleration of the body

Tables provide moment of inertia for common bodies such as cylinders, rods, and

rectangular solids. For bodies of arbitrary shape, methods of integration provide

a method to determine values of moment of inertia.

Definition of Mass Moment of Inertia about an Arbitrary Point, A, I^A_z,K

I^A_z,K = ∫ ∫ ρ r² dx dy = = ∫ ∫ r² dm

where I^A_z,K is the mass moment of inertia of the body about an arbitrary point, A

ρ is the mass per unit area of the body

r is the distance from the arbitrary point, A, to the element of mass, dm

dm equals ρ dx dy

dx dy is the element of area of the body