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Moment of Inertia of a Disc

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From a uniform square lamina of mass M and side L a circular hole of diameter L/2 whose rim passes through the centre of the square is cut the moment of inertia of them remaining part of the square about an axis perpendicular to the plane of lamina and passing through the centre is

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I_{1}

is moment of inertia of a square plate of uniform thickness about an axis perpendicular to the plane of plate and passing through its centre. From this square plate, a circular plate of maximum radius is cut and removed. If

I_{2}

is moment of inertia of this circular plate about an axis perpendicular to the plane of plate and passing through its centre then the ratio of

I_{1}

I_{2}

Q. From a disc of radius R and mass M, a circular hole of diameter R, whose rim passes through the centre is cut. What is the moment of inertia of the remaining part of disc about a perpendicular axis, passing through the centre?

Q. A symmetric lamina of mass M consists of a square shape with a semi-circular section over each of the edges of the square, as shown. The side of the square is

2 a

. The moment of inertia of the lamina about an axis through its centre of mass and perpendicular to the plane is

1.6

M a^{2}

. Calculate the moment of inertia of the lamina about the tangent AB in the plane of the lamina.

Q. A symmetric lamina of mass

M

consists of a square shape with a semicircular section over of the edge of the square as shown in figure. The side of the square is

2 a

. The moment of inertia of the lamina about an axis through its centre of mass and perpendicular to the plane is

1.6 M a^{2}

. The moment of inertia of the lamina about the tangent

A B

in the plane of the lamina is ...............

Q. A square plate of edge

\frac{a}{2}

is cut out from a uniform square plate of edge

^{'} a^{'}

as shown in figure. The mass of the remaining portion is

M

. The moment of inertia of the shaded portion about an axis passing through

^{'} O^{'}

(centre of the square of side a) and perpendicular to plane of the plate is:

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Moment of Inertia of a Disc

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