MOMENT OF INIRTIA OF HOLLOW CONE .Q2 MOMENT OF INIRTIA OF SOLID CONE WHOSE DENSITY IS VERING WITH RADIUS .
To find the moment of inertia of a hollow cone, you need to know the mass and dimensions of the cone. Let's start with the hollow cone.
1. Moment of Inertia of a Hollow Cone:
The moment of inertia (I) of a hollow cone can be calculated using the formula:
I = (3/10) * M * (r1^2 + r2^2)
Where:
- I represents the moment of inertia of the hollow cone.
- M is the mass of the cone.
- r1 and r2 are the radii of the cone's base and top, respectively.
2. Moment of Inertia of a Solid Cone with Varying Density:
To calculate the moment of inertia of a solid cone with varying density, you'll need to integrate the density function with respect to the radius.
I = ∫(r^2 * dm)
Where:
- I represents the moment of inertia of the solid cone.
- r is the radius of each elemental mass (dm).
- dm is the elemental mass.
- The integration should be done over the entire cone's radius.
Since you mentioned that the density is varying with the radius, you would need to have the density function expressed as a function of the radius (ρ(r)).
Once you have the density function, you can substitute it into the integral and solve for the moment of inertia.
It's important to note that the specific function/formula for the density is needed to proceed with the integration and obtain a numerical value for the moment of inertia.