Parallel Axis Theorem for a Solid Cylinder

length

500

radius

500

mass

0

axis

x =

0

, z =

0

moment of inertia

0

This Demonstration illustrates the parallel axis theorem for a solid cylinder. The parallel axis theorem states that

I

axis

=

I

cm

+m

2

r

, where

I

axis

is the moment of inertia of the object through the new axis,

I

cm

is the moment of inertia of the object through its center of mass,

m

is the mass of the object, and

r

is the perpendicular distance between the center of mass and the new axis. For a cylinder with an axis through the diameter of the shape,

I

cm

=

1

12

m(3

2

r

+

2

l

)

, where

l

is the length of the cylinder. You can vary the length, radius, and mass of the cylinder, and the location of the axis in the

x

-

z

plane.