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Title08_2_Moment_of_Inertia.pdf
Tags Rotation Rotation Around A Fixed Axis Perpendicular Classical Geometry
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Short Answer Questions :

Body Axis of rotation Moment of inertia

1. Disc of radius R
1) through its centre and
perpendicular 2

MR2


2) about the diameter
4

MR2


3) about a tangent to its own plane
4

MR5 2



4) tangent perpendicular to the
plane of 2

MR3 2


2. Annular ring or disc of outer
and inner radii R and r

1) through its centre and
perpendicular 2

)rR(M 22 +


2) about the diameter
4

)rR(M 22 +


3) about a tangent to its own plane
4

)rR5(M 22 +


3. Solid cylinder of length L
and

1) axis of cylinder
2

MR2



2) through its centre and
perpendicular to 













+

4
R

12
L

M
22



3) diameter of the face 












+

4
R

3
L

M
22



4. Thin rod of uniform length L
1) through its centre and
perpendicular 12

ML2



2) through one end and
perpendicular 3

ML2


5. Solid sphere of radius R 1) about a diameter
5
2

MR2

2) about a tangent 2MR
5
7



6. Hollow sphere of radius R about a diameter 2MR
3
2



7. Thin circular ring of radius R
1) perpendicular to its plane and
passing through its centre.

MR2

2) about its diameter
2

MR2


8. Hollow cylinder of radius R about axis of the cylinder MR2

9. Rectangular lamina of length l and
breadth b

1) through its centre
and perpendicular to its plane 













+

12
b

12
l

M
22




2) through its centre and parallel to
breadth along its own plane 12

Ml2



3) through its centre and parallel to
length along its own plane 12

Mb2



4) edge of the length in the plane of
the lamina 3

Mb2



5) edge of the breadth in the plane
of the lamina 3

Ml2




6) perpendicular to the plane of the
lamina and passing through the
mid point of the edge of the
length














+

3
b

12
l

M
22





7) perpendicular to the plane of the
lamina and passing through the
mid point of the edge of the
breadth














+

12
b

3
l

M
22



10. Plane elliptical lamina with the values
of axes 2a and 2b

Perpendicular to the plane of the
lamina and passing through its
centre

)ba(
4
M 22 +

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