Parallel axis theorem

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In physics, the  perpendicular axis theorem  (or  plane figure theorem ) can be used to determine the  moment of inertia  of a  rigid object  that lies entirely within a plane, about an axis perpendicular to the plane, given the moments of inertia of the object about two  perpendicular   axes  lying within the plane. The axes must all pass through a single point in the plane. Define perpendicular axes  {\displaystyle x} ,  {\displaystyle y} , and  {\displaystyle z}  (which meet at origin  {\displaystyle O} ) so that the body lies in the  {\displaystyle xy}  plane, and the  {\displaystyle z}  axis is perpendicular to the plane of the body. Let  I x ,  I y  and  I z  be moments of inertia about axis x, y, z respectively, the perpendicular axis theorem states that [1] {\displaystyle I_{z}=I_{x}+I_{y}} This rule can be applied with the  parallel axis theorem ...

In  physics , the  parallel axis theorem , also known as  Huygens–Steiner theorem , or just as  Steiner's theorem , [1]  after  Christiaan Huygens  and  Jakob Steiner , can be used to determine the  mass moment of inertia  or the  second moment of area  of a  rigid body  about any axis, given the body's moment of inertia about a  parallel  axis through the object's  center of gravity  and the  perpendicular   distance  between the axes. Mass moment of inertia [ edit ] The mass moment of inertia of a body around an axis can be determined from the mass moment of inertia around a parallel axis through the centre of mass. Suppose a body of mass  m  is made to rotate about an axis  z  passing through the body's  centre of gravity . The body has a moment of inertia  I cm  with respect to this axis. The parallel axis theorem states that if...