Moment of inertia and parallel and perpendicular laws

Moment of inertia and parallel and perpendicular laws

1. Moment of inertia Theorems

2. Radius of gyration M

3. Radius of gyration Distance from the axis of rotation at which the total mass of a body is assumed concentrated and at which the moment of inertia will be equal to the actual moment of inertia of the body.

4. A B C M a M Parallel-Axis Theorem If the moment of inertia about the axis passing through center of mass is known, then the moment of inertia through any other, parallel axis can be found.

5. Moment of inertia of a body about an axis is equal to the sum of the moment of inertia about a parallel axis passing through the centre of mass and product of mass of the body and square of the distance between the two axes. a

6. A B C D O a P m x

7. Perpendicular axis theorem. ABCD - plane lamina in xy plane Iy - Moment of inertia about y axis – in the plane of lamina Iz - Moment of inertia about z axis – perpendicular to xy plane Ix- Moment of inertia about x axis – in the plane of lamina Ix, Iz intersect at same point where Iz passes ┴ r to the plane lamina A B C D X Y Z

8. Perpendicular axis theorem. A B C D X Y Z Moment of inertia of a plane lamina about an axis perpendicular to its plane is equal to the sum of the moments of inertia of the lamina about two axes at right angles to each other, in its own plane and intersecting each other at the point where the perpendicular axis passes through it.

9. Perpendicular axis theorem. A B C D X Y Z P x Y r o