Moment of Inertia Formulas

Rod (Either End)

ml²/3

Rod (COM)

ml²/12

Ring (Perpendicular to Centre)

mR²

Ring (Perpendicular to any point in Circumference)

2mR²

Ring (Along Diameter)

mR²/2

Rectangular Plate (Along length)

ml²/3

Rectangular Plate (Along Breadth)

mb²/3

Rectangular Plate (Through centre parallel to length)

ml²/12

Rectangular Plate (Through centre parallel to breadth)

mb²/12

Rectangular Plate (Through Centre , Perpendicular to Plane)

m(l²+b²)/12

Rectangular Plate (Through Corner , Perpendicular to Plane)

m(l²+b²)/3

Hollow Cylinder

Same as ring

Uniform Disc (Perpendicular Through Centre)

mR²/2

Uniform Disc (Perpendicular Through Tangent)

3/2mR²

Uniform Disc (Through Diameter)

mR²/4

Uniform Disc (Tangent Parallel to Diameter)

5/4mR²

Hollow Sphere (Through Centre)

2/3mR²

Hollow Sphere (Tangential)

5/3mR²

Solid Sphere (Through Centre)

2/5mR²

Solid Sphere (Tangential)

7/5mR²

Solid Cone

3/10mR²

Isoceles Triangle (Along Diagonal)

ml²/12

Isoceles Triangle (Along Side)

ml²/6

Isoceles Triangle (Perpendicular to Vertex)

ml²/3

Solid Cylinder from a specific distance from it’s centre of mass

mR²/4 + ml²/12