Mass Moment of Inertia

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DETAILED METHOD OF MASS MOMENT OF INERTIA OF TRIANGULAR ELEMENT IN INVERTED POSITION
  MASS MOMENT OF INERTIA  Calculate the mass moment of inertia of the triangular plate about the  y -axis. Assume the  plate is made of a uniform material and has a mass of m . Solution: The mass moment of inertia about the  y -axis is given by     A zz   dAr dmr  I     22 B   The element of area in rectangular coordinate system is given by dydxdxdydA    The domain of the triangle is defined by   z ha xh y 00  The distance from the  y -axis is  x. Therefore, r=x . The mass moment of inertia about the  y -axis can be written as  yhah ha  123 303330 022          hady yhadxdy xdAr  I  h y yh y y yha x x A zz       For a uniform plate the density can be calculated using the total mass and total area of the  plate so that ahm Am 21      Therefore, the moment of inertia in terms of the total mass of the cone can be written as 612 23 maha  I   zz        
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