CBSE Class 11 Physics Motion Of System Of Particles Notes Set 02

inertia of the lamina about any two mutually perpendicular axes in its plane and intersecting each other at the point, where the perpendicular axis passes through the lamina.

Mathematically: I_z = I_x + I_y

Where x & y-axes lie in the plane of the Lamina and z-axis is perpendicular to its plane and passes through the point of intersecting of x and y axes.

.Theorem of parallel axes. It states that the moment of inertia of a rigid body about any axis is equal to moment of inertia of the body about a parallel axis through its center of mass plus the product of mass of the body and the square of the perpendicular distance between the axes.

Mathematically:  I = I_c + Mh², where is moment of inertia of the body about an axis through its centre of mass and is the perpendicular distance between the two axes.

i. M.I. of a rod about an axis through its c.m. and perpendicular to rod, I = x /12 ML²

ii. M.I. of a circular ring about an axis through its centre and perpendicular to its plane, I =  MR²

iii. M.I. of a circular disc about an axis through its centre and perpendicular to its plane, I = 1 /12 MR²

iv. M.I. of a right circular solid cylinder about its symmetry axis, I = x /12 ML²

v. M.I. of a right circular hollow cylinder about its axis = MR²

vi. M.I. of a solid sphere about its diameter, I = 2 /5 MR² 

vii. M.I. of spherical shell about its diameter,  I = 2 /3 MR²

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