I need the following formulas for a (square, a ring,cylinder,hollow cylinder,a triangle,disc, rod) etc..

1.Moment of inertia

2.Magnetic force

3.Electric force

4.Electric flux

5.Gravitational force

6.Centre of mass

7.Magnetic field intensity

8.Electric potential



11.Curved surface area

12.Total surface area

I will be happy to critique your analysis of these shapes.

I hope you are aware that not all of the combinations of objects or shapes and physical measurements make sense. For example, what is the electric potential of a triangle supposed to mean? And what does the "iit" mean in physics iit?

Sure! I can provide you with the formulas for each of these quantities. Here you go:

1. Moment of inertia:
For a square: I = (1/6) * (side length)^4
For a ring: I = (1/2) * M * R^2
For a cylinder: I = (1/2) * M * R^2
For a hollow cylinder: I = M * (R_outer^2 + R_inner^2)/2
For a triangle: I = (1/36) * M * (base)^2 * (height)^2
For a disc: I = (1/4) * M * R^2
For a rod: I = (1/12) * M * L^2

2. Magnetic force:
The formula for magnetic force depends on the situation and the quantities involved. Generally, the magnetic force acting on a charged particle moving in a magnetic field can be given by F = q * (v x B), where F is the force, q is the charge, v is the velocity, and B is the magnetic field.

3. Electric force:
The electric force between two charged objects can be calculated using Coulomb's law, which states that F = k * (Q1 * Q2) / r^2, where F is the force, Q1 and Q2 are the charges of the objects, r is the distance between them, and k is the Coulomb's constant (k ≈ 9 × 10^9 N·m²/C^2).

4. Electric flux:
The electric flux through a closed surface can be calculated using Gauss's law. The formula is Φ = E * A * cos(θ), where Φ is the electric flux, E is the electric field, A is the area of the surface, and θ is the angle between the electric field and the normal vector to the surface.

5. Gravitational force:
The gravitational force between two objects with masses m1 and m2 can be calculated using Newton's law of universal gravitation: F = G * (m1 * m2) / r^2, where F is the force, G is the gravitational constant (G ≈ 6.67430 × 10^-11 m³ kg^-1 s^-2), and r is the distance between the objects' centers of mass.

6. Centre of mass:
The center of mass of an object with multiple particles can be calculated using the formula (Xcm, Ycm, Zcm) = (Σ(mixi)/M, Σ(mi yi)/M, Σ(mi zi)/M), where (Xcm, Ycm, Zcm) are the coordinates of the center of mass, mi is the mass of the i-th particle, xi, yi, zi are the corresponding coordinates, and M is the total mass of the object.

7. Magnetic field intensity:
The magnetic field intensity near a current-carrying wire can be calculated using Ampere's law or the Biot-Savart law, depending on the situation. The formulas can vary, but one common formula is B = (μ0 * I) / (2π * r), where B is the magnetic field intensity, I is the current, r is the distance from the wire, and μ0 is the permeability of free space (μ0 ≈ 4π × 10^-7 T m A^-1).

8. Electric potential:
The electric potential at a point due to a point charge or a distribution of charges can be calculated using the formula V = k * (Q/r), where V is the electric potential, k is the Coulomb's constant (k ≈ 9 × 10^9 N·m²/C^2), Q is the charge, and r is the distance from the charge.

9. Area:
The formulas for area depend on the shape you are considering. For example:
- Square: A = side length^2
- Triangle: A = (base * height) / 2
- Disc: A = π * R^2
- Cylinder: A = 2π * R * (R + height)
- Hollow cylinder: A = 2π * (R_inner + R_outer) * (R_inner + R_outer + height)

10. Perimeter:
The formulas for perimeter also depend on the shape. For example:
- Square: P = 4 * side length
- Triangle: P = side1 + side2 + side3
- Disc: P = 2π * R
- Cylinder: P = 2π * R + 2 * height
- Hollow cylinder: P = 2π * (R_inner + R_outer)

11. Curved surface area:
For some shapes like cylinders and cones, there is a curved surface area. For example:
- Cylinder: CSA = 2π * R * height
- Cone: CSA = π * R * l, where l is the slant height

12. Total surface area:
Total surface area includes the sum of base(s) and curved surface area. For example:
- Cylinder: TSA = 2π * R * (R + height)
- Cone: TSA = π * R * (R + l), where l is the slant height