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# Moment of Inertia

The moment of inertia of is given by: Where we have:
m: mass
R: radius ( from the axis O to the object )

The following is a list of moment of inertia for some common homogeneous objects, where M stands for mass and the red line is the axis the objects rotating about.

 Object Illustration Moment of inertia Particle Md2 The distance between the particle and the axis is d. Bar ML2/3 The length of the bar is L Bar ML2/12 The length of the bar is L Rectangular plate ML2/12 The length of the plate is L and is orthogonal to the axis. Rectangular plate M(L2 + W2)/12 L is the length and W is the width Circular plate MR2/2 R is the radius of the ring Circular plate MR2/4 R is the radius of the ring Ring MR2 R is the radius of the ring Cylinder MR2/2 R is the radius of the caps Cylinder MR2/4 + ML2/12 R is the radius of the caps and L is the height of the cylinder Spherical surface 2MR2/3 R is the radius Sphere 2MR2/5 R is the radius

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