Moment of inertia of rod about two different axis

Derivation to find out moment of inertia of a thin uniform rod

1. Moment of inertia of thin uniform rod

2. Thin uniform rod M ,l o dx x Mass per unit length= Mass of dx = Moment of inertia of dx = -l/ 2 +l/ 2 C M

3. Thin uniform rod o dx x Total Moment of inertia = -l/ 2 +l/ 2

4. Thin uniform rod A B C M a=l/2

5. Rectangular lamina

6. Rectangular lamina A B C D M l b Y Y’ X X’ dx x Mass per unit area= Mass of strip= Moment of inertia of strip along YY ’ Total Moment of inertia along YY ’,

7. Rectangular lamina A B C D M l b Y Y’ X X’ dy y Mass per unit area= Mass of strip= Moment of inertia of strip along XX’ Total Moment of inertia along XX’,

8. Rectangular lamina