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

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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