Some Typical Bodies and their Moments of Inertia: Notes pdf ppt Engineering Mechanics

 Moments of Inertia:

Moment of inertia is the name given to rotational inertia, the rotational analog of mass for linear motion. It appears in the relationships for the dynamics of rotational motion. The moment of inertia must be specified with respect to a chosen axis of rotation. For a point mass the moment of inertia is just the mass times the square of perpendicular distance to the rotation axis, I = mr². That point mass relationship becomes the basis for all other moments of inertia since any object can be built up from a collection of point masses.

Some Typical Bodies and their Moments of Inertia:

Cylinder:

Thin-walled hollow cylinder:

Moments of Inertia for a thin-walled hollow cylinder is comparable with the point mass (1) and can be expressed as:

I = m r²            (3a)

where

m = mass of the hollow (kg, slugs)

r = distance between axis and the thin walled hollow (m, ft)

r_o = distance between axis and outside hollow (m, ft)

Hollow cylinder:

I = 1/2 m (r_i² + r_o²)               (3b)

where

m = mass of hollow (kg, slugs)

r_i = distance between axis and inside hollow (m, ft)

r_o = distance between axis and outside hollow (m, ft)

Solid cylinder:

I = 1/2 m r²                  (3c)

where

m = mass of cylinder (kg, slugs)

r = distance between axis and outside cylinder (m, ft)

Circular Disk:

I = 1/2 m r²                (3d)

where

m = mass of disk (kg, slugs)

r = distance between axis and outside disk (m, ft)

Sphere:

Thin-walled hollow sphere:

I = 2/3 m r²          (4a)

where

m = mass of sphere hollow (kg, slugs)

r = distance between axis and hollow (m, ft)

Solid sphere:

I = 2/5 m r²             (4b)

where

m = mass of sphere (kg, slugs)

r = radius in sphere (m, ft)

Rectangular Plane:

Moments of Inertia for a rectangular plane with axis through center can be expressed as

I = 1/12 m (a² + b²)              (5)

where

a, b = short and long sides

Moments of Inertia for a rectangular plane with axis along edge can be expressed as

I = 1/3 m a²             (5b)

Slender Rod:

Moments of Inertia for a slender rod with axis through center can be expressed as

I = 1/12 m L²          (6)

where

L = length of rod

Moments of Inertia for a slender rod with axis through end can be expressed as

I = 1/3 m L²              (6b)

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