How do we calculate the moment of inertia?

How do we calculate the moment of inertia?

the moment of inertia of a body with respect to a point is equal to half the sum of its moments of inertia in relation to three perpendicular axes (O x , O y , O z ) passing through the point.

How to calculate the moment of inertia of a ball?

I = 2m r2/5: moment of inertia of the ball with respect to an axis passing through G.

What is a principal axis of inertia?

If instead of taking any point A, we take the center ofinertia G, the base B’, is the central base ofinertia and the moments A’, B’ and VS‘ are the central moments ofinertia. Note: The axes characteristics of a solid (symmetries) are axes main ofinertia.

How to calculate inertia of an axis?

The Quadratic Moment or Inertia (we will commonly use this last term to designate this concept) corresponds to a surface (inscribed in a plane) multiplied by the square of the distance separating any point of the plane from the center of gravity of this surface.

How to calculate the moment of inertia of a solid?

There are an infinite number of combinations depending on the shape of the solid, the placement of its axis and its homogeneity. The calculation form below allows you to calculate the moment of inertia of some simple forms of revolutions around their main axis such as: and the full cone.

How to calculate the moment of inertia of an object?

Moreover, the calculation formulas used to establish the moment of inertia of an object, it is necessary to use formulas which are composed of very particular mathematical signs and very complex to reproduce using a simple keyboard.

How to calculate the moment of inertia of a cylinder?

It is also possible to determine the moment of inertia along any axis Ox perpendicular to the axis of revolution Oz of the cylinder. It is: expresses a density (mass per unit volume). . Note that the expression of the moment of inertia as a function of its mass and the radius of its base does not depend on the height of the cone. .

How to calculate the moment of inertia of a cylindrical layer?

The volume dV of a cylindrical layer is: dV = 2π.rL.dr Therefore, the mass of the shell is: This expression is substituted in the definition of the moment of inertia: The above equation states that the moment of inertia of the cylinder does not depend on its length, but only on its mass and its radius.