From a circular disc of radius $R$ and mass $9M$, a small disc of mass $M$ and radius $\frac{R}{3}$ is removed concentrically. The moment of inertia of the remaining disc about an axis perpendicular to the plane of the disc and passing through its centre is
Mass of the disc = 9M Mass of removed portion of disc = M
The moment of inertia of the complete disc about an axis passing through its centre O and perpendcular to its plane is $I_1=\frac{9}{2}MR^2$ Now, the moment of inertia of the disc with removed portion $I_{2}=\frac{1}{2}M\left(\frac{R}{3}\right)^{2}=\frac{1}{18}MR^{2}$ Therefore, moment of inertia of the remaining portion of disc about O is $I=I_1-I_2=9\frac{MR^2}{2}-\frac{MR^2}{18}=\frac{40MR^2}{9}$
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Top Questions on System of Particles & Rotational Motion
The system of particles refers to the extended body which is considered a rigid body most of the time for simple or easy understanding. A rigid body is a body with a perfectly definite and unchangeable shape.
The distance between the pair of particles in such a body does not replace or alter. Rotational motion can be described as the motion of a rigid body originates in such a manner that all of its particles move in a circle about an axis with a common angular velocity.
The few common examples of rotational motion are the motion of the blade of a windmill and periodic motion.
