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Kinetic energy in rotational motion
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Rotational Inertia or Momentum Inertia (转动惯量):
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If the mass density is uniform,  |
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Rotational inertial of a thin rod |
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Axis at center:  |
Axis at end:  |
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Rotation of a cylinder about its symmetry axis |
Solid cylinder: 
Thin wall:  |
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Finding the moment of inertia for common shapes |
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Rotation of a uniform sphere about a center axis |
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Extended bodies and the Parallel Axis Theorem |
Parallel-Axis Theorem (平行轴定理):
 is the rotational inertia about the axis through the center of mass. M is the mass of the rigid body. 
 is the lowest rotational inertia for a rigid body.
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